A long straight wire of circular cross section of radius 'a' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point $a/2$ above the surface of wire to that of a point $a/2$ below its surface is (A) 4:1 (B) 1...
CBSE CLASS 12 • PHYSICS • CHAPTER 04
Moving Charges and Magnetism
253 distinct questions across 335 board paper set appearances (2022–2026).
A wire of length $L$ is bent round into (i) a square coil having $N$ turns and (ii) a circular coil having $N$ turns. The coil in both cases is free to turn about a vertical axis coinciding with the plane of the coil, in a uniform, horizontal magnetic field and carry the same currents. Find the rati...
A galvanometer is used to detect or/and measure small currents in an electrical circuit. It essentially works on the fact that a current-carrying coil experiences a deflecting torque when placed in a magnetic field. This deflection in the coil can be measured and it is related to the current flowing...
(i) Define mutual inductance of a pair of coils. Write its SI unit.
(ii) A long solenoid of radius $R$ and length $L$ has $n$ turns per unit length. A circular loop of radius $r (<R)$ is placed inside at the centre of the solenoid such that its axis coincides with the axis of the solenoid. Obtain th...
Assertion (A) : The cylindrical soft iron core in a moving coil galvanometer only makes the magnetic field radial and does not affect the strength of the magnetic field.
Reason (R) : In a moving coil galvanometer, the plane of the coil is always perpendicular to the magnetic field.
(a) Depict the variation of electric field (\vec{E}) and magnetic field (\vec{B}) with respect to the direction of propagation of an electromagnetic wave. Write their two important characteristics. (b) Show that \frac{1}{\sqrt{\varepsilon_0 \mu_0}} gives the velocity of an electromagnetic wave in fr...
Suppose particles 1 and 2 enter the magnetic field $\vec{B} = B_0 \hat{k}$ with velocities $\vec{v}_1 = v_1 \hat{i}$ and $\vec{v}_2 = v_2 \hat{i}$. Then :
(A) both particles revolve clockwise
(B) both particles revolve anticlockwise
(C) particle 1 revolves clockwise while particle 2 revolves anticlo...
(a) The figure given below shows three straight long parallel conductors (1), (2) and (3) kept in x-y plane, carrying currents 2I, I and 3I respectively as shown in figure. Find the magnitude and direction of : (i) net magnetic field at a point on conductor (1) and (ii) net magnetic force acting on ...
Write the expression for the magnetic field due to a current element in vector form. Consider a $1\text{ cm}$ segment of a wire, centered at the origin, carrying a current of $10\text{ A}$ in positive x-direction. Calculate the magnetic field $\vec{B}$ at a point $(1\text{ m}, 1\text{ m}, 0)$.
Two infinitely long straight conductors lie along x-axis and y-axis in the plane of the page. If they carry current I each along $+x$-axis and $+y$-axis respectively, the net magnetic field at a point with position vector $\vec{r} = $3\hat{i} + 4\hat{j}$\text{ m}$ will be :
(A) $\frac{\mu_0 I}{6\pi}...
A particle of mass $m$ and charge $q$ experiences a force $\vec{F}_e$ in an electric field $\vec{E}$ and it is directed along the field. When the particle is moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$, it experiences a force $\vec{F}_B$, that is perpendicular to both $\vec{v}$ and ...
A long straight wire is held vertically and carries a steady current in upward direction. The shape of magnetic field lines produced by the current-carrying wire are :
(A) horizontal straight lines directed radially out from the wire.
(B) straight lines parallel to the current-carrying wire.
(C) con...
A piece of a diamagnetic material, free to move when placed in a uniform magnetic field :
(A) moves along the field
(B) moves opposite to the field
(C) moves perpendicular to the field
(D) does not move at all
A proton and an $\alpha$-particle enter with the same velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$ such that $\vec{v} \perp \vec{B}$. The ratio of the radii of their paths is :
(A) $2$
(B) $\frac{1}{2}$
(C) $\frac{1}{4}$
(D) $4$
A metal rod of length $50\text{ cm}$ is held vertically and moved with a velocity of $10\text{ m/s}$ towards east. The horizontal component of the Earth's magnetic field at the place is $0\cdot4\text{ G}$. The emf induced across the ends of the rod is :
(A) $0\cdot1\text{ mV}$
(B) $0\cdot2\text{ mV}...
Assertion (A) : A charged particle is moving with velocity $v$ in x-y plane, making an angle $\theta$ ($0 < \theta < \frac{\pi}{2}$) with x-axis. If a uniform magnetic field $\vec{B}$ is applied in the region, along y-axis, the particle will move in a helical path with its axis parallel to x-axis.
R...
(a) (i) With the help of a labelled diagram, explain the principle of working of a moving coil galvanometer. Write the purpose of using (i) radial magnetic field, and (ii) soft iron core, in it.
(ii) Define current sensitivity of a galvanometer. "Increasing the current sensitivity may not necessaril...
Assertion (A) : The deflection in a galvanometer is directly proportional to the current passing through it. Reason (R) : The coil of a galvanometer is suspended in a uniform radial magnetic field.
(a) (i) What is the source of force acting on a current-carrying conductor placed in a magnetic field ? Obtain the expression for force acting between two long straight parallel conductors carrying steady currents and hence define 'ampere'.
Assertion (A) : An electron and a proton enter with the same momentum $\vec{p}$ in a magnetic field $\vec{B}$ such that $\vec{p} \perp \vec{B}$. Then both describe a circular path of the same radius.
Reason (R) : The radius of the circular path described by the charged particle (charge q, mass m) mo...
(a) Two long, straight, parallel conductors carry steady currents in opposite directions. Explain the nature of the force of interaction between them. Obtain an expression for the magnitude of the force between the two conductors. Hence define one ampere. OR (b) Obtain an expression for the torque $...
(a) (i) A particle of mass m and charge q is moving with a velocity $\vec{v}$ in a magnetic field $\vec{B}$ as shown in the figure. Show that it follows a helical path. Hence, obtain its frequency of revolution. (ii) In a hydrogen atom, the electron moves in an orbit of radius $2 \text{ \AA}$ making...
Assertion (A) : The torque acting on a current carrying coil is maximum when it is suspended in a radial magnetic field.
Reason (R) : The torque tends to rotate the coil on its own axis.
A current carrying circular loop of magnetic moment $\vec{M}$ is suspended in a vertical plane in an external magnetic field $\vec{B}$ such that its plane is normal to $\vec{B}$. The work done in rotating this loop by $45^\circ$ about an axis perpendicular to $\vec{B}$ is closest to :
(A) $-0.3 \te...
Consider a solenoid of length $l$ and area of cross-section $A$ with fixed number of turns. The self-inductance of the solenoid will increase if :
(A) both $l$ and $A$ are increased
(B) $l$ is decreased and $A$ is increased
(C) $l$ is increased and $A$ is decreased
(D) both $l$ and $A$ are decreased
Assertion (A): A proton and an electron enter a uniform magnetic field $\vec{B}$ with the same momentum $\vec{p}$ such that $\vec{p}$ is perpendicular to $\vec{B}$. They describe circular paths of the same radius.
Reason (R): In a magnetic field, orbital radius r is equal to $\frac{\text{p}}{\text{q...
Assertion (A) : The energy of a charged particle moving in a magnetic field does not change. Reason (R) : It is because the work done by the magnetic force on the charge moving in a magnetic field is zero.
Derive an expression for magnetic force $\vec{F}$ acting on a straight conductor of length L carrying current I in an external magnetic field $\vec{B}$. Is it valid when the conductor is in zig-zag form ? Justify.
The best way to increase current sensitivity of a galvanometer is by
(A) increasing number of turns of the coil
(B) increasing area of coil and magnitic field strength
(C) decreasing area of coil and magnetic field strength
(D) increasing torsional constant of the hair spring
Derive an expression for the magnetic field $\vec{B}$, due to a circular coil of N turns, each of radius $r$ carrying current $I$, at a distance '$x$' from the centre along its axis.
A plane electromagnetic wave travels through a medium and the magnetic field associated with it is given by $B = 5 \times 10^{-8} \sin (3 \times 10^{10} t - 150 x) \text{ T}$ where x is in metres and t is in seconds. The velocity of the wave is : (A) $2.0 \times 10^8 \text{ m s}^{-1}$ (B) $4.5 \time...
(a) A circular coil of 30 turns and radius $8.0\text{ cm}$ carrying a current of $6\text{ A}$ is suspended vertically in a uniform horizontal magnetic field of $1.0\text{ T}$. The field lines make an angle of $30^{\circ}$ with the plane of the coil. Calculate the magnitude of the external torque tha...
A charged particle +q in an electric field $\vec{E}$ experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field $\vec{B}$. But this magnetic force is perpendicular to ...
Two particles of masses $m_1$ and $m_2$ having charges $q_1$ and $q_2$ respectively are projected with the same velocity in a region of uniform magnetic field $\vec{B}$ pointing vertically upward. If they describe circular paths as shown in the figure, one may conclude that :
(A) $\frac{m_1}{m_2} > ...
The magnetic field in a plane electromagnetic wave travelling in glass ($n = 1\cdot 5$) is given by
$B_y = (2 \times 10^{-7}\text{ T}) \sin (\alpha x + 1\cdot 5 \times 10^{11} t)$
where $x$ is in metres and $t$ is in seconds. The value of $\alpha$ is :
(A) $0\cdot 5 \times 10^3\text{ m}^{-1}$
(B) $6...
(ii) A circular coil of $100$ turns and radius $\left$\frac{10}{\sqrt{\pi}}\right$ \text{ cm}$ carrying current of $5\cdot0 \text{ A}$ is suspended vertically in a uniform horizontal magnetic field of $2\cdot0 \text{ T}$. The field makes an angle $30^\circ$ with the normal to the coil. Calculate :
...
A current-element ($I\vec{dl}$) of mass per unit length ($m$) is held in air as shown in the figure. After withdrawing the support, it will remain suspended in its position, when subjected to an external magnetic field $\vec{B}$ equal to :
(A) $\frac{mgdl}{I}\hat{k}$
(B) $\frac{mg}{I}\hat{j}$
(C) $-...
An electron is moving in a circular path in a uniform magnetic field of $3\cdot14 \times 10^{-4}\text{ T}$. Its period of revolution will be approximately :
(A) $0\cdot11\text{ }\mu\text{s}$
(B) $0\cdot28\text{ }\mu\text{s}$
(C) $0\cdot014\text{ }\mu\text{s}$
(D) $0\cdot024\text{ }\mu\text{s}$
Two identical circular coils A and B of radius $10\text{ cm}$ each are placed concentrically and mutually perpendicular in XY and YZ planes respectively. Currents of $1\text{ A}$ and $\sqrt{3}\text{ A}$ flow anticlockwise in the coils as seen from YZ plane. Find the magnitude of the net magnetic fie...
A galvanometer is an instrument used to show the direction and strength of the current passing through it. In a galvanometer, a coil placed in a magnetic field experiences a torque and hence gets deflected when a current passes through it. The name is derived from the surname of Italian scientist L....
A rectangular coil of area A is kept in a uniform magnetic field $\vec{B}$ such that the plane of the coil makes an angle $\alpha$ with $\vec{B}$. The magnetic flux linked with the coil is :
(A) $BA\sin\alpha$
(B) $BA\cos\alpha$
(C) $BA$
(D) zero
Depict the variation of electric and magnetic fields in an electromagnetic wave as it propagates along z-axis. In a plane electromagnetic wave in free space, the electric field oscillates sinusoidally at a frequency of $1.5 \times 10^{10} \text{ Hz}$ with amplitude $36 \text{ Vm}^{-1}$. Find :
(a) t...
An electron (mass $9 \times 10^{-31}\text{ kg}$ and charge $1.6 \times 10^{-19}\text{ C}$) is moving in a circle with a speed of $3.2 \times 10^7\text{ m/s}$ in a magnetic field of $4.5 \times 10^{-4}\text{ T}$ perpendicular to it. Calculate :
(i) the radius of the circular path,
(ii) its frequency ...
A 1 cm segment of a wire lying along x-axis carries current of 0.5 A along +x direction. A magnetic field $\vec{B} = (0.4 \text{ mT}) \hat{j} + (0.6 \text{ mT}) \hat{k}$ is switched on, in the region. The force acting on the segment is
(A) $$2\hat{j} + 3\hat{k}$ \text{ mN}$
(B) $$-3\hat{j} + 2\hat{k...
You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be
(A) 2592
(B) 2866
(C) 2976
(D) 3140
(a) (i) A proton moving with velocity $\vec{\text{V}}$ in a non-uniform magnetic field traces a path as shown in the figure. The path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points P, Q and R? What can you say about r...
A $1\text{ cm}$ straight segment of a conductor carrying $1\text{ A}$ current in $x$ direction lies symmetrically at origin of Cartesian coordinate system. The magnetic field due to this segment at point $(1\text{m}, 1\text{m}, 0)$ is
(A) $1.0 \times 10^{-9} \hat{k}\text{ T}$
(B) $-1.0 \times 10^{-9...
A 10 cm long wire lies along y-axis. It carries a current of 1.0 A in positive y-direction. A magnetic field $\vec{B} = (5 \text{ mT}) \hat{j} - (8 \text{ mT}) \hat{k}$ exists in the region. The force on the wire is : (A) $(0.8 \text{ mN}) \hat{i}$ (B) $-(0.8 \text{ mN}) \hat{i}$ (C) $(80 \text{ mN}...
OR (b) (i) What is current sensitivity of a galvanometer? Show how the current sensitivity of a galvanometer may be increased. "Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity." Explain. (ii) A moving coil galvanometer has a resistance $15 \t...
The electric field E associated with an electromagnetic wave is represented by
$E_y = E_0\sin$kx - \omega t$$
Which of the following statements is correct ?
(A) The wave is propagating along $+x$-axis.
(B) The wave is propagating along $+z$-axis.
(C) The magnetic field $\vec{B}$ of the wave is actin...
A small circular loop of area $\frac{6}{\pi}\text{ cm}^2$ is placed inside a long solenoid at its centre such that its axis makes an angle of $60^{\circ}$ with the axis of the solenoid. The number of turns per cm is $10$ in the solenoid. The current in the solenoid changes uniformly from $5\text{ A}...
The electric field in an electromagnetic wave in vacuum is given by :
$\vec{E} = (6.3 \text{ N/C}) [\cos (1.5 \text{ rad/m}) y + (4.5 \times 10^8 \text{ rad/s}) t] \hat{i}$
(a) Find the wavelength and frequency of the wave.
(b) What is the amplitude of the magnetic field of the wave ?
(c) Write an e...
An electron with velocity $\vec{v} = $v_x \hat{i} + v_y \hat{j}$$ moves through a magnetic field $\vec{B} = $B_x \hat{i} - B_y \hat{j}$$. The force $\vec{F}$ on the electron is : ($e$ is the magnitude of its charge)
(a) $- e (v_x B_y - v_y B_x) \hat{k}$
(b) $e (v_x B_y - v_y B_x) \hat{k}$
(c) $- e (...
A planar loop is rotated in a magnetic field about an axis perpendicular to the field. The polarity of induced emf changes once in each :
(a) 1 revolution
(b) $\left(\frac{1}{2}\right)$ revolution
(c) $\left(\frac{1}{4}\right)$ revolution
(d) $\left(\frac{3}{4}\right)$ revolution
Two identical bars, one of a paramagnetic material and another of a diamagnetic material are kept in a uniform magnetic field. Show diagrammatically the modifications in the pattern of magnetic field in each case. How are the two materials affected by increase in temperature ?
A long straight wire of circular cross-section (radius a) carries a steady current I. The current is uniformly distributed across this cross-section. The magnitude of the magnetic field produced at a point at a distance $(a/2)$ from the axis of the wire will be
(A) Zero
(B) $\frac{\mu_0 \text{I}}{...
The torque on the coil remains constant irrespective of the coil's orientation during rotation due to
(A) use of soft iron core which increases the magnetic field.
(B) radial magnetic field
(C) hair spring which provides the counter torque
(D) eddy current in the iron core which causes damping.
A moving coil galvanometer has a coil with area of cross-section $4.0 \times 10^{-3} ext{ m}^2$ and number of turns $50$. The coil is rotating in a magnetic field of $0.25 ext{ T}$. The torque acting on the coil when a current of $5 ext{ A}$ passes through it is
(A) $1.0 ext{ N m}$
(B) $2.0 ext{ N m...
A straight conductor lies along $x$-axis. It carries a current of $10\text{ A}$ along $+x$ direction. The magnetic field $\vec{B}$ due to $1\text{ cm}$ segment of this conductor, centred at the origin, at a point $(0, 1\text{ m}, 0)$ is
(A) $(1\text{ nT}) \hat{j}$
(B) $(10\text{ nT}) \hat{k}$
(C) $-...
A moving coil galvanometer has a coil with area of cross-section $4.0 \times 10^{-3} \text{ m}^2$ and number of turns $50$. The coil is rotating in a magnetic field of $0.25 \text{ T}$. The torque acting on the coil when a current of $5 \text{ A}$ passes through it is
(A) $1.0 \text{ N m}$
(B) $2.0 ...
A circular loop has radius $R$ and carries current $I$ as shown in figure. In order that the net magnetic field at the centre of the loop is zero, the current in wire $AB$ should have magnitude
(A) $2\pi I$, along $+\text{X}-\text{axis}$
(B) $2\pi I$, along $-\text{X}-\text{axis}$
(C) $\pi I$, along...
A straight long wire lying along $y$-axis, carries a current of $1\text{ A}$ along $-y$ direction. The magnetic field due to the conductor at a point $(50\text{ cm}, 0, 0)$ will point along.
(A) $z$-axis
(B) $-z$-axis
(C) $x$-axis
(D) $-x$-axis
A magnet held vertically, with its north pole down is dropped along the axis of a closed solenoid placed vertically on a table. If the observer looks down from the top,
(A) the induced current will flow in the anticlockwise direction.
(B) the induced current will flow in the clockwise direction.
(C)...
The expression of magnetic fields associated with four electromagnetic waves are given below :
I. $B_1 = (4 \times 10^{-6}\text{ T}) \sin [0.7 \times 10^3x + 1.4 \times 10^{11}\text{ t}]$
II. $B_2 = (2 \times 10^{-7}\text{ T}) \sin [0.6 \times 10^3x + 1.5 \times 10^{11}\text{ t}]$
III. $B_3 = (3 \ti...
A straight conductor lies along $x$-axis and carries a current of $2\text{ A}$ along $+x$ direction. The magnetic field at a point $(0, 40\text{ cm}, 0)$ due to $1\text{ cm}$ length of conductor centered at the origin points along.
(A) $y$-axis
(B) $-y$-axis
(C) $z$-axis
(D) $-z$-axis
Derive an expression for the magnetic field $\vec{\text{B}}$, due to a circular coil of N turns, each of radius r carrying current I, at a distance '$x$' from the centre along its axis.
A person is standing facing geographic north and a vertical wire in front of him is carrying a current in downward direction. The direction of magnetic field at a point on the right side of wire is
(A) South
(B) East
(C) West
(D) North
A square loop of side $10\text{ cm}$ is placed vertically in the east-west plane in a uniform magnetic field of $0\cdot2\text{ T}$ directed along the north-east direction. If the magnetic field is reduced to zero in $0\cdot4\text{ s}$ at a steady rate, the magnitude of induced emf will be :
(A) $5\...
Moving coil galvanometer is a sensitive instrument used for detecting current in a circuit. Its working is based on the fact that when current is passed through a coil suspended freely in a magnetic field, a deflecting torque acts on it whose magnitude is directly proportional to the strength of the...
(ii) Which of the following does not affect the current sensitivity of a moving coil galvanometer ? (A) Number of turns in the coil (B) Area of the coil (C) Strength of the magnetic field (D) Resistance of the coil
A moving coil galvanometer has parameters as $N = 125$ turns, $I = 20 \text{ mA}$, $B = 0\cdot5 \text{ T}$ and $A = 400 \text{ mm}^2$.
The deflecting torque on the coil of the galvanometer is :
(A) $20 \text{ Nm}$
(B) $0\cdot1 \text{ Nm}$
(C) $5 \times 10^{-4} \text{ Nm}$
(D) $3 \times 10^{-6} \text...
(a) (i) State Biot-Savarts law. Using it, derive an expression for the magnetic field B at the centre of a current-carrying circular loop. (ii) A circular coil of 100 turns has a radius of 10 cm and carries a current of 5 A. Calculate the magnetic field at the centre of the coil.
(a) A straight vertical wire carries a current of $3 \text{ A}$ upward along $+z$ axis. Calculate the magnitude and direction of the magnetic field at a point $15 \text{ cm}$ away from the wire on $+x$-axis. Name the rule used to find the direction of magnetic field.
(b) A flexible loop of irregular...
(a) Briefly explain how Lenz's law is consistent with the law of conservation of energy.
(b) Considering the case of the magnetic field $B$ inside a solenoid of length $l$, area of cross-section $A$, prove that magnetic energy per unit volume is $\frac{B^2}{$2 \mu_0$}$.
A charged particle is moving horizontally with a velocity $\vec{v}$. If a uniform magnetic field $\vec{B}$ directly vertically up is set-up in the region, the particle moves in a circle of radius R in anti-clockwise direction. (i) The charged particle exhibiting this motion is (A) electron (B) proto...
A square loop of side 50 cm is placed in a uniform magnetic field of 3.0 T acting perpendicular to the plane of the loop. If the loop is rotated through an angle of 90° in 0.3 s, the value of emf induced in the loop would be : (A) 0.25 V (B) 0.50 V (C) 0.75 V (D) 1.0 V
(a) A circular coil of 30 turns and radius 8.0 cm carrying a current of 6 A is suspended vertically in a uniform horizontal magnetic field of 1.0 T. The field lines make an angle of 30° with the plane of the coil. Calculate the magnitude of the external torque that must be applied to prevent the coi...
A charged particle +q in an electric field $\vec{\text{E}}$ experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field $\vec{\text{B}}$. But this magnetic force is per...
A metallic rod of $1\text{ m}$ length is rotated with a frequency of $40\text{ rev/s}$, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius $1\text{ m}$, about an axis passing through the centre and perpendicular to the plane of the ring. A ...
A plane electromagnetic wave travels through a medium and the magnetic field associated with it is given by $B = 5 \times 10^{-8} \sin (3 \times 10^{10} \text{ t} - 150 \text{ x}) \text{ T}$ where x is in metres and t is in seconds. The velocity of the wave is : (A) $2.0 \times 10^8 \text{ ms}^{-1}$...
Two identical conductors 1 and 2 are placed on two frictionless conducting rails R and S in a uniform magnetic field directed vertically downward into the plane of the page. If conductor 1 is moved with a constant velocity in the direction as shown in figure, the force on conductor 2 will be along :...
OR (b) A rectangular loop of sides $l$ and b and resistance 'R' is kept in a region in which the magnetic field varies as $B = B_0 \sin \omega t$. (i) Derive expression for the emf induced in the loop. (ii) Find the effective value of current that flows in the loop.
A closely wound long solenoid of self-inductance L is cut into two identical solenoids. The value of self-inductance of each small solenoid will be :
(A) $\frac{\text{L}}{2}$
(B) $2\text{L}$
(C) $3\text{L}$
(D) $4\text{L}$
Two particles of masses $\text{m}_1$ and $\text{m}_2$ having charges $\text{q}_1$ and $\text{q}_2$ respectively are projected with the same velocity in a region of uniform magnetic field $\vec{\text{B}}$ pointing vertically upward. If they describe circular paths as shown in the figure, one may conc...
A conducting rectangular loop of area $5\text{ cm}^2$ and resistance $4\ \Omega$ is removed from a region of uniform magnetic field, acting normal to the plane of the loop. The value of induced current I in the loop varies with time t, as shown in the figure.
Find :
(a) total charge that passed thro...
Four long straight thin wires are held vertically at the corners A, B, C and D of a square of side '$a$', kept on a table and carry equal current '$I$'. The wire at A carries current in upward direction whereas the current in the remaining wires flows in downward direction. The net magnetic field at...
The magnetic flux through a loop placed in a magnetic field can be changed by changing :
(A) area of the loop only
(B) the value of magnetic field only
(C) orientation of the loop in the magnetic field only
(D) any one or more of the factors given in (A), (B) and (C)
A plane circular coil is rotated about its vertical diameter with a constant angular speed $\omega$ in a uniform horizontal magnetic field. Initially the plane of the coil is parallel to the magnetic field. Draw plots showing the variation of the following physical quantities as the function of $\om...
A long solenoid of length $L$ and radius $r_1$ having $N_1$ turns is surrounded symmetrically by a coil of radius $r_2$ ($> r_1$) having $N_2$ turns ($N_2 \ll N_1$) around its mid-point. Derive an expression for the mutual inductance of solenoid and coil. Is $M_{12} = M_{21}$ valid in this case ?
(a) (i) A rectangular loop of sides a and b carrying current I is placed in a magnetic field $\vec{B}$ such that its area vector $\vec{A}$ makes an angle $\theta$ with $\vec{B}$. With the help of a suitable diagram, show that the torque $\vec{\tau}$ acting on the loop is given by $\vec{\tau} = \vec{...
A rectangular loop of size $5\text{ cm} \times 8\text{ cm}$ is lying in x-y plane in a uniform magnetic field $\vec{B} = (2\cdot0\text{ T}) \hat{k}$. The total magnetic flux linked with the loop is :
(A) $80\text{ Wb}$
(B) $16\text{ Wb}$
(C) $8 \times 10^{-2}\text{ Wb}$
(D) $8 \times 10^{-3}\text{ W...
A square loop of side $10\text{ cm}$, free to rotate about a vertical axis coinciding with its one arm, is initially held perpendicular to a uniform horizontal magnetic field of $0 \cdot 2\text{ T}$. If it is rotated at the uniform speed of $60\text{ rpm}$, find the emf induced in the loop.
A square loop of side $0.50\text{ m}$ is placed in a uniform magnetic field of $0.4\text{ T}$ perpendicular to the plane of the loop. The loop is rotated through an angle of $60^{\circ}$ in $0.2\text{ s}$. The value of emf induced in the loop will be :
(A) $5\text{ V}$
(B) $3.5\text{ V}$
(C) $2.5\te...
The magnetic field in a plane electromagnetic wave travelling in glass ($n = 1.5$) is given by
$B_y = (2 \times 10^{-7}\text{ T}) \sin (\alpha x + 1.5 \times 10^{11} \text{ t})$
where x is in metres and t is in seconds. The value of $\alpha$ is :
(A) $0.5 \times 10^3\text{ m}^{-1}$
(B) $6.0 \times 1...
A charged particle is moving in a uniform magnetic field $\vec{B}$ with a constant speed $v$ in a circular path of radius $r$. Which of the following graphs represents the variation of radius of the circle, with the magnitude of magnetic field $\vec{B}$?
(A)
(B)
(C)
(D)
(a) Derive the expression for the magnetic field (near its centre) due to an air-filled long solenoid carrying a current I and having n number of turns per unit length.
(b) A charged particle moving with velocity $\vec{v}$ enters a region of uniform magnetic field $\vec{B}$. The force acting on it i...
Two identical circular coils A and B of radius $10\text{ cm}$ each are placed concentrically and mutually perpendicular in $\text{XY}$ and $\text{YZ}$ planes respectively. Currents of $1\text{ A}$ and $\sqrt{3}\text{ A}$ flow anticlockwise in the coils as seen from $\text{YZ}$ plane. Find the magnit...
OR
An alpha particle (mass $6\cdot4 \times 10^{-27}\text{ kg}$) moves in a circular path with a speed of $6\cdot28 \times 10^5\text{ m/s}$ in a uniform magnetic field of $3\cdot14 \times 10^{-3}\text{ T}$. The radius of the path is :
(A) $1\cdot00\text{ m}$
(B) $2\cdot00\text{ m}$
(C) $3\cdot00\text...
An alpha particle (mass $6.4 \times 10^{-27}\text{ kg}$) moves in a circular path with a speed of $6.28 \times 10^5\text{ m/s}$ in a uniform magnetic field of $3.14 \times 10^{-3}\text{ T}$. The radius of the path is :
(A) $1.00\text{ m}$
(B) $2.00\text{ m}$
(C) $3.00\text{ m}$
(D) $4.00\text{ m}$
A negative ion enters a region of uniform magnetic field $\vec{B}$ as shown in the figure.
It will :
(A) go straight, undeviated
(B) describe a circular path
(C) describe a semicircular path
(D) describe a helical path
A current-element ($I \vec{\text{d}l}$) of mass per unit length (m) is held in air as shown in the figure. After withdrawing the support, it will remain suspended in its position, when subjected to an external magnetic field $\vec{\text{B}}$ equal to :
(A) $\frac{mg\text{d}l}{I}\hat{\text{k}}$
(B)...
A negative ion enters a region of uniform magnetic field $\vec{B}$ as shown in the figure.\nIt will :\n(A) go straight, undeviated\n(B) describe a circular path\n(C) describe a semicircular path\n(D) describe a helical path
OR\nAn alpha particle (mass $6\cdot 4 \times 10^{-27}\text{ kg}$) moves in a circular path with a speed of $6\cdot 28 \times 10^5\text{ m/s}$ in a uniform magnetic field of $3\cdot 14 \times 10^{-3}\text{ T}$. The radius of the path is :\n(A) $1\cdot 00\text{ m}$\n(B) $2\cdot 00\text{ m}$\n(C) $3\cd...
Two small identical magnets are allowed to fall freely one through a vertical solenoid of $20\text{ m}$ made up of copper and another in air through the same vertical distance. The time taken by the two magnets to fall will be<br><br>(A) same in both the cases.<br>(B) more for the magnet falling in ...
If a point sized object having charge $1\text{ C}$ and mass $1\text{ g}$ is projected with velocity of $2\hat{\imath}\text{ m/s}$ from a point $(0,2\text{cm},0)$ in the region of magnetic field $-0.1\hat{k}\text{ T}$ which spreads in the first quadrant.\n(A) What will be the shape of the path follow...
A solenoid has a core of material with relative permeability $200$. The windings of the solenoid are insulated from the core and carry a current of $1\text{ A}$. If the number of turns is $2000$ per metre, calculate\n(A) magnetic intensity,\n(B) magnetic field &
(C) magnetisation
A conducting coil of $50$ turns and area $\frac{5}{\pi}\text{ cm}^2$ is rotating along the axis of solenoid of length $50\text{cm}$ and $2000$ turns, carrying current of $5\text{ A}$. What will be the value of maximum emf generated?
The acceleration of a particle of mass ' $m$' and charge ' $q$' moving with uniform speed $v$ at right angles to a magnetic field $B$ is given by :
(A) $\frac{qB}{vm}$
(B) $\frac{qBv}{m}$
(C) $\frac{qv}{Bm}$
(D) $\text{Bqvm}$
Which of the following will not increase the output voltage in a generator ?
(A) Rotating the coil rapidly
(B) Changing the material of the coil
(C) Increasing the area of coil
(D) Increasing the magnetic field through the coil
A current-carrying conductor produces a magnetic field around it. A current-carrying conductor when placed in an external magnetic field also experiences a magnetic force. It implies that the force between two parallel current-carrying conductors is mutual and magnetic in nature.
Imagine a long stra...
If the current in the two wires X and Y flows from west to east direction, the force acting on per unit length of wire Y will be :
(A) $\frac{\mu_0 I_1 I_2}{2 r}$, pointing vertically downward.
(B) $\frac{\mu_0 I_1 I_2}{2 \pi r}$, pointing vertically downward.
(C) $\frac{\mu_0 I_1 I_2}{2 r}$, pointi...
The net magnetic field will be zero at a point between the two wires X and Y when the distance (d) of the point from wire X is :
(A) $\frac{I_1 r}{I_1 + I_2}$, $I_1$ and $I_2$ flow in the same direction.
(B) $\frac{I_1 r}{I_1 + I_2}$, $I_1$ and $I_2$ flow in the opposite direction.
(C) $\frac{I_1 r}...
(iv) (b) Suppose wires X and Y are arranged perpendicular to each other, in horizontal plane, with their centres coinciding (without touching). Wire X carries current $I$ from west to east and wire Y carries current $I$ from south to north. Then the net magnetic field at a point equidistant (distanc...
(a) (i) What is the difference between an electric field and a magnetic field ?
(ii) Briefly explain the condition under which a particle (charge $q$ and mass $m$) moving through a magnetic field $\vec{B}$ with a velocity $\vec{v}$ :
(I) describes a circular path.
(II) describes a helical path.
(III...
OR
(b) (i) State the principle of working of a moving coil galvanometer. Briefly describe its construction and working.
(ii) A galvanometer of $100 ext{ }\Omega$ shows full scale deflection for a current of $10 ext{ mA}$. How will you convert it into a voltmeter of range $(0 - 10 ext{ V})$ ? What wi...
A particle having charge $+q$ enters a uniform magnetic field $\vec{B}$ as shown in the figure. The particle will describe :
(A) a circular path in XZ plane
(B) a semicircular path in XY plane
(C) a helical path with its axis parallel to Y-axis
(D) a semicircular path in YZ plane
(a) Write vector form of Biot-Savart law.
(b) Two insulated long straight wires, each carrying $2\cdot0\text{ A}$ current are kept along $xx'$ and $yy'$ axis as shown in the figure. Find the magnitude and direction of resultant magnetic field at point $\text{P }(4\text{m}, 5\text{m})$.
(a) (i) State Lenz's law and explain how this law is a consequence of conservation of energy principle.
(ii) A square shaped loop of side $\frac{l}{2}$ is initially lying outside a region of uniform magnetic field $\vec{B}$ as shown in the figure. The loop is moved towards right with a constant vel...
A particle with charge q moving with velocity $\vec{v} = v_0 \hat{i}$ enters a region with magnetic field $\vec{B} = B_1 \hat{j} + B_2 \hat{k}$. The magnitude of force experienced by the particle is :
(A) $q v_0 (B_1 + B_2)$
(B) $q \sqrt{v_0} (B_1 + B_2)$
(C) $q v_0 \sqrt{(B_1^2 + B_2^2)}$
(D) $q \s...
(a) A charged particle $q$ moving with a velocity $\vec{v}$ is subjected to a uniform magnetic field $\vec{B}$ acting perpendicular to $\vec{v}$. If a uniform electric field $\vec{E}$ is also set up in the region along the direction of $\vec{B}$, describe the path followed by the particle and draw i...
(ii) A square shaped loop of side $\frac{l}{2}$ is initially lying outside a region of uniform magnetic field $\vec{B}$ as shown in the figure. The loop is moved towards right with a constant velocity $\vec{v}$ till it goes out of the region of magnetic field.\n\n(I) What will be the directions of i...
A particle of mass $m$ and charge $q$ moves along y-axis in a region in which a uniform magnetic field $\vec{B}$ is pointing along x-axis. The Lorentz force acting on the charge will point along :
(A) x-axis
(B) y-axis
(C) z-axis
(D) negative z-axis
(a) In which cases does a charged particle not experience a force in a magnetic field ?
(b) A square loop MNPK of side '$l$' carrying a current '$I_2$' is kept close to a long straight wire in the same plane and the wire carries a steady current $I_1$ as shown in the figure. Obtain the magnitude of...
(iv) (a) A galvanometer is converted into a voltmeter of range $(0 - \text{V})$ by connecting with it, a resistance $R_1$. If $R_1$ is replaced by $R_2$, the range becomes $(0 - 2\text{ V})$. The resistance of the galvanometer is :
(A) $(R_2 - 2R_1)$
(B) $(R_2 - R_1)$
(C) $(R_1 + R_2)$
(D) $(R_1 - 2...
A circular coil of wire having $200$ turns, each of radius $4.0\text{ cm}$ is placed in a horizontal plane. It carries a current of $0.40\text{ A}$ in clockwise direction. Find the magnitude and direction of the magnetic field at the centre of the coil.
(a) Use Ampere's law to derive the expression for the magnetic field due to a long straight current carrying wire of infinite length.
(b) Why is Ampere's law used for the derivation in (a) above and not Biot-Savart's law ? Explain.
(a) A galvanometer is converted into a voltmeter of range $(0 - \text{V})$ by connecting with it, a resistance $R_1$. If $R_1$ is replaced by $R_2$, the range becomes $(0 - 2\text{ V})$. The resistance of the galvanometer is :
(A) $(R_2 - 2R_1)$
(B) $(R_2 - R_1)$
(C) $(R_1 + R_2)$
(D) $(R_1 - 2R_2)$...
A current of $5\text{ A}$ is passing along $+X$ direction through a wire lying along X-axis. Find the magnetic field $\vec{B}$ at a point $\vec{r} = $3\hat{i} + 4\hat{j}$\text{ m}$ due to $1\text{ cm}$ element of the wire, centered at origin.
(b) A current of $5\text{ mA}$ flows through a galvanometer. Its coil has $100$ turns, each of area of cross-section $18\text{ cm}^2$ and is suspended in a magnetic field $0\cdot20\text{ T}$. The deflecting torque acting on the coil will be :
(A) $3\cdot6 \times 10^{-3}\text{ Nm}$
(B) $1\cdot8 \time...
The value of magnetic field at point $O$ in the given figure is :
(A) $\frac{\mu_0 I}{2\pi R}$
(B) $\frac{\mu_0 I}{\pi R}$
(C) $\frac{\mu_0 I}{4R}$
(D) $\frac{\mu_0 I}{R}$
A straight conductor is carrying a current of $2\text{ A}$ in +x direction along it. A uniform magnetic field $\vec{\text{B}} = (0.6\,\hat{\text{j}} + 0.8\,\hat{\text{k}})\text{ T}$ is switched on, in the region. The force acting on $10\text{ cm}$ length of the conductor is :
(A) $(0.12\,\hat{\text{...
(a) (i) Write Biot-Savart's law in vector form.
(ii) Two identical circular coils A and B, each of radius $R$, carrying currents $I$ and $\sqrt{3}I$ respectively, are placed concentrically in $\text{XY}$ and $\text{YZ}$ planes respectively. Find the magnitude and direction of the net magnetic field ...
In a circular loop of radius $R$, current $I$ enters at point $A$ and exits at point $B$, as shown in the figure. The value of the magnetic field at the centre $O$ of the loop is :
(A) $\frac{\mu_0 I}{R}$
(B) zero
(C) $\frac{\mu_0 I}{2R}$
(D) $\frac{\mu_0 I}{4R}$
(a) (i) Write Biot-Savart's law in vector form.
(ii) Two identical circular coils $ ext{A}$ and $ ext{B}$, each of radius $ ext{R}$, carrying currents $ ext{I}$ and $\sqrt{3} ext{ I}$ respectively, are placed concentrically in $ ext{XY}$ and $ ext{YZ}$ planes respectively. Find the magnitude and dir...
(a) Two concentric circular coils of radii $r_1$ and $r_2$ ($r_2 \gg r_1$) are placed coaxially with their centres coinciding. If a current $I$ is passed through the outer coil, obtain the expression for mutual inductance of the arrangement.
(b) The current in a solenoid decreases steadily from $6\t...
(b) (i) (I) Write Ampere's circuital law in mathematical form and explain the terms used.
(II) As the current carrying solenoid is made longer, the magnetic field produced outside it approaches zero. Why ?
(III) A flexible loop of irregular shape carrying current when located in an external magnetic...
(a) (i) Write Biot-Savart's law in vector form.
(ii) Two identical circular coils A and B, each of radius R, carrying currents I and $\sqrt{3}\text{I}$ respectively, are placed concentrically in XY and YZ planes respectively. Find the magnitude and direction of the net magnetic field at their common...
A rectangular loop of area vector $\vec{A} = [\hat{i} + \sqrt{3}\hat{j}] \times 10^{-2}\text{ m}^2$ is placed in a magnetic field $\vec{B} = [4.0t^2 + 2.0]\hat{i}$, where $B$ is in tesla and $t$ in seconds. At $t = 1.0\text{ s}$, the magnitude of induced emf in the loop is :
(A) $80\text{ mV}$
(B) $...
A rectangular loop ($4\text{ cm} \times 5\text{ cm}$) of wire carrying current of $0\cdot25\text{ A}$ is placed in a magnetic field $\vec{B} = [(0\cdot20\text{ T})\hat{j} + (0\cdot50\text{ T})\hat{k}]$ such that outward unit vector normal to the plane of the loop is $$0\cdot80\hat{i} - 0\cdot60\hat{...
Consider two long, straight, parallel conductors A and B separated by a distance $d$. They carry steady current $I$ in the same direction. The force acting on unit length of conductor B due to conductor A is :
(A) $\frac{\mu_0}{2\pi} \frac{I^2}{d}$ and is attractive
(B) $\frac{\mu_0}{2\pi} \frac{I^2...
A rectangular loop of area vector $\vec{A} = [\hat{i} + \sqrt{3} \hat{j}] \times 10^{-2} \text{ m}^2$ is placed in a magnetic field $\vec{B} = [4\cdot0t^2 + 2\cdot0] \hat{i}$, where B is in tesla and t in seconds. At t = 1\cdot0 s, the magnitude of induced emf in the loop is :
(A) $80 \text{ mV}$
(B...
A circular loop of wire of radius $7.0\text{ cm}$ carrying a current of $1.0\text{ A}$ is placed in a magnetic field $\vec{B} = (0.5\hat{i} + 0.4\hat{k})\text{ T}$ such that the outward unit vector normal to the plane of the loop is $[0.60\hat{i} + 0.80\hat{j}\,]$. Calculate :
(a) the magnetic momen...
A rectangular loop of area vector $\vec{A} = [\hat{i} + \sqrt{3}\text{ }\hat{j}] \times 10^{-2}\text{ m}^2$ is placed in a magnetic field $\vec{B} = [4\cdot0t^2 + 2\cdot0]\text{ }\hat{i}$, where B is in tesla and t in seconds. At t = $1\cdot0\text{ s}$, the magnitude of induced emf in the loop is :
...
A rectangular loop ($1\text{ cm} \times 5\text{ cm}$) of wire carrying current of $0.4\text{ A}$ is placed in a magnetic field $\vec{B} = (0.03\,\hat{i} + 0.04\,\hat{k})\text{ T}$ such that the outward unit vector normal to the plane of the loop is $(0.60\,\hat{i} - 0.80\,\hat{j})$. Calculate :
(a) ...
A loop carrying a current $I$ clockwise is placed in $x - y$ plane, in a uniform magnetic field directed along $z$-axis. The tendency of the loop will be to :
(A) move along x-axis
(B) move along y-axis
(C) shrink
(D) expand
A $10\text{ cm}$ long wire lies along $y$-axis. It carries a current of $1.0\text{ A}$ in positive $y$-direction. A magnetic field $\vec{B} = (5\text{ mT}) \hat{j} - (8\text{ mT}) \hat{k}$ exists in the region. The force on the wire is :
(A) $(0.8\text{ mN}) \hat{i}$
(B) $-(0.8\text{ mN}) \hat{i}$
(...
A proton with kinetic energy $1\cdot3384 \times 10^{-14} \text{ J}$ moving horizontally from north to south, enters a uniform magnetic field $B$ of $2\cdot0 \text{ mT}$ directed eastward. Calculate :
(a) the speed of the proton
(b) the magnitude of acceleration of the proton
(c) the radius of the pa...
A coil has 100 turns, each of area $0.05 \text{ m}^2$ and total resistance $1.5 \Omega$. It is inserted at an instant in a magnetic field of 90 mT, with its axis parallel to the field. The charge induced in the coil at that instant is :
(A) 3.0 mC
(B) 0.30 C
(C) 0.45 C
(D) 1.5 C
Using Biot-Savart law, derive expression for the magnetic field $(\vec{\text{B}})$ due to a circular current carrying loop at a point on its axis and hence at its centre.
(a) Show that the energy required to build up the current $\text{I}$ in a coil of inductance $\text{L}$ is $\frac{1}{2}\text{LI}^2$. (b) Considering the case of magnetic field produced by air-filled current carrying solenoid, show that the magnetic energy density of a magnetic field $\text{B}$ is $\...
(a) (i) A proton moving with velocity $\vec{V}$ in a non-uniform magnetic field traces a path as shown in the figure.\nThe path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points P, Q and R ? What can you say about relati...
A $1\text{ cm}$ segment of a wire lying along x-axis carries current of $0.5\text{ A}$ along $+x$ direction. A magnetic field $\vec{B} = (0.4\text{ mT})\,\hat{j} + (0.6\text{ mT})\,\hat{k}$ is switched on, in the region. The force acting on the segment is
(A) $$2\hat{j} + 3\hat{k}$\text{ mN}$
(B) $...
A circular coil of diameter $15\text{ mm}$ having $300$ turns is placed in a magnetic field of $30\text{ mT}$ such that the plane of the coil is perpendicular to the direction of magnetic field. The magnetic field is reduced uniformly to zero in $20\text{ ms}$ and again increased uniformly to $30\te...
You are required to design an air-filled solenoid of inductance $0.016\text{ H}$ having a length $0.81\text{ m}$ and radius $0.02\text{ m}$. The number of turns in the solenoid should be
(A) $2592$
(B) $2866$
(C) $2976$
(D) $3140$
(a) Define magnetic moment of a current-carrying coil. Write its SI unit. (b) A coil of $60$ turns and area $1.5 \times 10^{-3} \, \text{m}^2$ carrying $2 \text{A}$ current lies in a vertical plane. It experiences a torque of $0.12 \, \text{Nm}$ when placed in a uniform horizontal magnetic field. Th...
Consider two long co-axial solenoids $S_1$ and $S_2$, each of length $l$ ($>> r_2$) and of radius $r_1$ and $r_2$ ($r_2 > r_1$). The number of turns per unit length are $n_1$ and $n_2$ respectively. Derive an expression for mutual inductance $M_{12}$ of solenoid $S_1$ with respect to solenoid $S_2$....
(b) (i) Derive an expression for the torque acting on a rectangular current loop suspended in a uniform magnetic field. (ii) A charged particle is moving in a circular path with velocity $\vec{\text{V}}$ in a uniform magnetic field $\vec{\text{B}}$. It is made to pass through a sheet of lead and as ...
A 1 cm straight segment of a conductor carrying 1 A current in x direction lies symmetrically at origin of Cartesian coordinate system. The magnetic field due to this segment at point (1m, 1m, 0) is (A) $1.0 \times 10^{-9} \hat{k} \text{ T}$ (B) $-1.0 \times 10^{-9} \hat{k} \text{ T}$ (C) $\frac{5.0...
The magnetic field due to a small magnetic dipole of dipole moment 'M' at a distance 'r' from the centre along the axis of the dipole is given by (A) $\frac{\mu_0}{4\pi} \times \frac{2M}{r^3}$ (B) $\frac{\mu_0}{4\pi} \times \frac{M}{r^3}$ (C) $\frac{\mu_0}{4\pi} \times \frac{M}{2r^3}$ (D) $\frac{\mu...
(a) In a region of a uniform electric field $\vec{\text{E}}$, a negatively charged particle is moving with a constant velocity $\vec{v} = -v_0 \hat{i}$ near a long straight conductor coinciding with $\text{XX}'$ axis and carrying current $\text{I}$ towards $-\text{X}$ axis. The particle remains at a...
(ii) A point charge q is moving with velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$. Find the work done by the magnetic force on the charge.
(iii) Explain the necessary conditions in which the trajectory of a charged particle is helical in a uniform magnetic field.
OR
(b) (i) A current car...
Two long solenoids of radii $r_1$ and $r_2$ ($> r_1$) and number of turns per unit length $n_1$ and $n_2$ respectively are co-axially wrapped one over the other. The ratio of self-inductance of inner solenoid to their mutual inductance is ---
(A) $\frac{n_1}{n_2}$
(B) $\frac{n_2}{n_1}$
(C) $\frac{n_...
A coil of an ac generator, having $100$ turns and area $0.1\text{ m}^2$ each, rotates at half a rotation per second in a magnetic field of $0.02\text{ T}$. The maximum emf generated in the coil is
(A) $0.31\text{ V}$
(B) $0.20\text{ V}$
(C) $0.63\text{ V}$
(D) $0.10\text{ V}$
(b) Two infinitely long conductors kept along $XX'$ and $YY'$ axes are carrying current $I_1$ and $I_2$ along $-X$ axis and $-Y$ axis respectively. Find the magnitude and direction of the net magnetic field produced at point $P(X, Y)$.
(a) In a region of a uniform electric field $\vec{E}$, a negatively charged particle is moving with a constant velocity $\vec{v} = -v_0\hat{i}$ near a long straight conductor coinciding with XX' axis and carrying current I towards -X axis. The particle remains at a distance d from the conductor. (i)...
A particle of mass $m$ and charge $q$ moving with a velocity $\vec{v}$ at right angle to a magnetic field $\vec{B}$, experiences a force $\vec{F}$. Another particle of mass $2m$ and charge $2q$ enters the same field $\vec{B}$ with a velocity $\frac{\vec{v}}{2}$, in the same direction. This particle ...
A $5.0 ext{ cm}$ long wire carrying $1.0 ext{ A}$ current is kept in a region in which a uniform magnetic field of $0.3 ext{ T}$ is applied perpendicular to the length of the wire. The magnitude of the force acting on the wire is -
(A) zero
(B) $0.45 ext{ N}$
(C) $0.03 ext{ N}$
(D) $0.015 ext{ N}$
Assertion (A) : Only a continuous change of magnetic flux will maintain an induced emf in a coil.
Reason (R) : An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic field that induces the current.
(a) Write one point of similarity and one point of difference between magnetic field and the electrostatic field.
(b) A wire of length $l$ is first bent into a circular loop and then into a circular coil of two turns. For the same current passing through them, find the ratio of the magnetic fields a...
(a) (A) When a current passes through a conductor it produces a magnetic field.
(i) State the right-hand thumb rule that gives the direction of the magnetic field.
(ii) How does the magnetic field vary with the distance from the conductor?
(iii) Name the factors (other than the distance) which affec...
(B) Derive an expression for torque acting as a rectangular loop carrying a steady current when placed in a uniform magnetic field.
A piece of wire bent in the form of a circular loop A carries a current I. The wire is then bent into a circular loop B of two turns and carries the same current. The ratio of magnetic fields at the centre of loop A to that of loop B will be : (A) $\frac{1}{16}$ (B) 16 (C) 4 (D) $\frac{1}{4}$
A conducting circular loop is placed in a uniform magnetic field $B = 50 \text{ mT}$ with its plane perpendicular to the magnetic field. The radius of the loop is made to shrink at a constant rate of $1 \text{ mm s}^{-1}$. At the instant the radius of the loop is $4 \text{ cm}$, the induced emf in t...
The electric and magnetic fields of electromagnetic waves are :
(A) In the same phase and perpendicular to each other.
(B) In the same phase and not perpendicular to each other.
(C) Not in the same phase but are perpendicular to each other.
(D) Neither in the same phase nor perpendicular to each oth...
A bar magnet of magnetic moment $2.5 ext{ J T}^{-1}$ lies aligned with the direction of a uniform magnetic field of $0.32 ext{ T}$.
(a) Find the amount of work done to turn the magnet so as to align its magnetic moment (i) normal to the field direction, and (ii) opposite to the field direction.
(b) ...
A circular coil with cross-sectional area $0\cdot2\text{ cm}^2$ carries a current of $4\text{ A}$. It is kept in a uniform magnetic field of magnitude $0\cdot5\text{ T}$ normal to the plane of the coil. Calculate :
(a) the net force on the coil.
(b) the torque on the coil.
(c) the average force on e...
Q19. P and Q are two identical charged particles each of mass $4 \times 10^{-26}\text{ kg}$ and charge $4.8 \times 10^{-19}\text{ C}$, each moving with the same speed of $2.4 \times 10^5\text{ m/s}$ as shown in the figure. The two particles are equidistant ($0.5\text{ m}$) from the vertical Y-axis. ...
Q26. A boy is holding a smooth, hollow and non-conducting pipe vertically with charged spherical ball of mass 10 g carrying a charge of +10 mC inside it which is free to move along the axis of the pipe. The boy is moving the pipe from East to West direction in the presence of magnetic field of 2T. W...
Case Study Based Question: Motion of Charge in Magnetic Field. An electron with speed $v_o \ll c$ moves in a circle of radius $r_o$ in a uniform magnetic field. This electron is able to traverse a circular path as the magnetic force acting on the electron is
(i) If the speed of the electron is now doubled to $2v_o$. The radius of the circle will change to (A) $4r_o$ (B) $2r_o$ (C) $r_o$ (D) $r_o/2$
(ii) If $v = 2v_o$, then the time required for one revolution of the electron ($T_o$) will change to (A) $4T_o$ (B) $2T_o$ (C) $T_o$ (D) $T_o/2$
(iii) A ch...
A circular coil of radius $10\text{ cm}$ is placed in a magnetic field $\vec{B} = (1.0 \hat{i} + 0.5 \hat{j})\text{ mT}$ such that the outward unit vector normal to the surface of the coil is $(0.6 \hat{i} + 0.8 \hat{j})$. The magnetic flux linked with the coil is :
(A) $0.314 \mu\text{Wb}$
(B) $3.1...
A 100-turn coil of radius 1.6 cm and resistance 5.0 $\Omega$ is co-axial with a solenoid of 250 turns/cm and radius 1.8 cm. The solenoid current drops from 1.5 A to zero in 25 ms. Calculate the current induced in the coil in this duration. (Take $\pi^2$ = 10)
A rectangular loop of sides $10\text{ cm} \times 20\text{ cm}$ is kept outside a region of uniform magnetic field $|\vec{B}| = 5\text{ mT}$ as shown in the figure. The loop is moved with the velocity of $5\text{ cm/s}$ till it goes completely out of the magnetic field. (a) Plot a graph showing varia...
The emf induced in a coil rotating in a magnetic field does not depend upon the following :
(A) Area of the coil
(B) Resistance of the coil
(C) Number of turns in the coil
(D) Angular speed of rotation of the coil
A circular coil of radius $10\text{ cm}$ is placed in a magnetic field $\vec{\text{B}} = (1.0 \hat{\text{i}} + 0.5 \hat{\text{j}}) \text{ mT}$ such that the outward unit vector normal to the surface of the coil is $(0.6 \hat{\text{i}} + 0.8 \hat{\text{j}})$. The magnetic flux linked with the coil is...
In four regions I, II, III and IV, the magnetic field is given by :
I. $\text{B}_\text{y} = \text{B}_0 \sin \text{kz}$
II. $\text{B}_\text{y} = \text{B}_0 \cos \text{kz}$
III. $\text{B}_\text{y} = \text{B}_0 \sin $\text{kz} - \omega\text{t}$$
IV. $\text{B}_\text{y} = \text{B}_0 \sin \text{kz} + \tex...
(b) (i) What is current sensitivity of a galvanometer? Show how the current sensitivity of a galvanometer may be increased. "Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity." Explain. (ii) A moving coil galvanometer has a resistance $15 \; \O...
A bar magnet of magnetic moment $4 \text{ J T}^{-1}$ is kept along the direction of magnetic field of $0.4 \text{ T}$. The work done to rotate the magnet through an angle of $90^{\circ}$ is :
(A) Zero
(B) $-1.6 \text{ J}$
(C) $-0.2 \text{ J}$
(D) $1.6 \text{ J}$
Assertion (A) : A magnetic field does not interact with a moving charge. Reason (R) : A moving charge does not produce a magnetic field.
(a) (i) Discuss the motion of a charged particle of mass m and charge q in a uniform magnetic field $\vec{B}$ with initial velocity $\vec{v}$ (1) at an angle $\theta$ with field direction, (2) perpendicular to the field direction ($\theta = 90^{\circ}$), and (3) parallel to the field direction ($\th...
A straight wire of length $1.0\text{ m}$ is placed along x-axis, in a region with magnetic field $\vec{B} = $3\hat{i} + 2\hat{j}$\text{ T}$. A current of $2.0\text{ A}$ flows in the wire along $+x$ direction. The magnetic force acting on the wire is :
(A) $2.0\text{ N}$, along $z$-axis
(B) $2.0\text...
Two circular loops of areas A and 4A carry currents 2I and I respectively. The magnetic fields at their centres will be in the ratio of : (A) 3 : 1 (B) 4 : 1 (C) 1 : 1 (D) 1 : 2
The magnetic field of an electromagnetic wave is represented as $B_x = B_0 \sin$ky - \omega t$$. It means that the wave propagation direction and wave vector k are respectively : (A) $+z\,\text{axis}, \frac{2\pi}{v}$ (B) $-z\,\text{axis}, \frac{2\pi}{T}$ (C) $+y\,\text{axis}, \frac{2\pi}{\lambda}$ (...
The current sensitivity of a galvanometer does not depend on the : (A) magnetic field in which the coil is suspended. (B) current flowing in the coil. (C) torsional constant of the spring. (D) area of the coil.
A particle of mass m and charge q is moving in a magnetic field $\vec{B}$ with a velocity $\vec{v}$. Discuss, giving reasons, the shape of its trajectory when the angle between $\vec{v}$ and $\vec{B}$ is: (a) $0^\circ$ (b) $90^\circ$ (c) $120^\circ$
Two circular coils of radius $R$ each and having equal number of turns $N$, carry equal currents $I$ in the same direction. They are placed coaxially at a distance $2\sqrt{3}$ $R$. Find the magnitude and direction of the net magnetic field produced at the midpoint of the line joining their centres.
A rod PQ of resistance R lies across frictionless conducting rails in a constant uniform magnetic field $\vec{B}$, as shown in the figure. Assuming that the rails have negligible resistance, the force required to pull the rod to the right at constant velocity $\vec{v}$ is:
(A) 0
(B) $Blv$
(C) $\frac...
A current of $5 \text{ A}$ is flowing in a wire of length $1.5 \text{ cm}$. A force of $7.5 \text{ mN}$ acts on it when it is placed in a uniform magnetic field of $0.2 \text{ T}$. The angle between the magnetic field and the direction of current is :
(A) $30^{\circ}$ (B) $45^{\circ}$ (C) $60^{\circ...
An electron is passing through a region and experiences no force. Under what condition is it possible when the region has (a) only the magnetic field, and (b) both the electric and the magnetic fields ? Justify your answers.
A $2.0 \text{ cm}$ segment of wire, carrying $5.0 \text{ A}$ current in positive y-direction lies along y-axis, as shown in the figure. The magnetic field at a point $(3 \text{ m}, 4 \text{ m}, 0)$ due to this segment (part of a circuit) is : (A) $(0.12 \text{ nT}) \hat{j}$ (B) $-(0.10 \text{ nT}) \...
A circular loop of wire, carrying a current 'I' is lying in xy-plane with its centre coinciding with the origin. It is subjected to a uniform magnetic field pointing along $+z$-axis. The loop will : (A) move along x-axis (B) move along $-y$-axis (C) move along z-axis (D) remain stationary
A 2.0 cm segment of wire, carrying 5.0 A current in positive y-direction lies along y-axis, as shown in the figure. The magnetic field at a point (3 m, 4 m, 0) due to this segment (part of a circuit) is :
(A) (0.12 nT) $\hat{j}$
(B) -(0.10 nT) $\hat{j}$
(C) -(0.24 nT) $\hat{k}$
(D) (0.24 nT) $\hat{k...
Two thin long parallel wires separated by a distance 'a' carry current 'I' in opposite directions. The wires will :
(A) Repel each other with a force $\frac{\mu_0 I^2}{2\pi a^2}$, per unit length.
(B) Attract each other with a force $\frac{\mu_0 I^2}{2\pi a^2}$, per unit length.
(C) Attract each oth...
A rectangular loop of area $\vec{A}$, carrying current I, is placed in a uniform magnetic field $\vec{B}$. With the help of a suitable diagram, derive an expression, in vector form, for the torque acting on the loop.
The electric field in an electromagnetic wave in vacuum is given by : $\vec{E} = (6\cdot3 \text{ N/C}) [\cos (1\cdot5 \text{ rad/m}) y + (4\cdot5 \times 10^8 \text{ rad/s}) t] \hat{i}$ (a) Find the wavelength and frequency of the wave. (b) What is the amplitude of the magnetic field of the wave? (c)...
A $2.0\;\text{cm}$ segment of wire, carrying $5.0\;\text{A}$ current in positive y-direction lies along y-axis, as shown in the figure. The magnetic field at a point $(3\;\text{m}, 4\;\text{m}, 0)$ due to this segment (part of a circuit) is :
(A) $(0.12\;\text{nT}) \hat{j}$
(B) $-(0.10\;\text{nT}) \...
A straight wire is kept horizontally along east-west direction. If a steady current flows in wire from east to west, the magnetic field at a point above the wire will point towards
(A) East
(B) West
(C) North
(D) South
A coil of N turns is placed in a magnetic field $\vec{B}$ such that $\vec{B}$ is perpendicular to the plane of the coil. B changes with time as $B = B_0 \cos\left$\frac{2\pi}{T}t\right$$ where T is time period. The magnitude of emf induced in the coil will be maximum at
(A) $t = \frac{nT}{8}$
(B) $t...
A circular loop of radius $10\text{ cm}$ carrying current of $1.0\text{ A}$ lies in $x$-$y$ plane. A long straight wire lies in the same plane parallel to $x$-axis at a distance of $20\text{ cm}$ as shown in figure. Find the direction and value of current that has to be maintained in the wire so tha...
A particle of mass m and charge q is moving with velocity $\vec{v} = v_x \hat{i} + v_y \hat{j}$. If it is subjected to a magnetic field $\vec{B} = B_0 \hat{i}$, it will move in a - (A) straight line path (B) circular path (C) helical path (D) parabolic path
A coil of N turns is placed in a magnetic field $\vec{B}$ such that $\vec{B}$ is perpendicular to the plane of the coil. $\vec{B}$ changes with time as $B = B_0 \cos \left$\frac{2\pi}{T}t\right$$ where T is time period. The magnitude of emf induced in the coil will be maximum at
(A) $t = \frac{nT}{8...
Two long insulated straight wires carrying currents of 3 A and 5 A are arranged in XY plane as shown in figure. Find the magnitude and direction of the net magnetic fields at points $P_1$(2m, 2m) and $P_2$(−1m, 1m).
Two long straight parallel conductors A and B, kept at a distance r, carry current I in opposite directions. A third identical conductor C, kept at a distance $(\frac{r}{3})$ from A carry current $I_1$ in the same direction as in A. The net magnetic force on unit length of C is
(A) $\frac{3\mu_0 I I...
A coil of N turns is placed in a magnetic field $\vec{\text{B}}$ such that $\vec{\text{B}}$ is perpendicular to the plane of the coil. $\vec{\text{B}}$ changes with time as $\text{B} = \text{B}_0 \cos\left$\frac{2\pi}{\text{T}}\text{t}\right$$ where $\text{T}$ is time period. The magnitude of emf in...
A particle of mass $\text{m}$ and charge $\text{q}$ describes a circular path of radius $\text{R}$ in a magnetic field. If its mass and charge were $2 \text{ m}$ and $\frac{\text{q}}{2}$ respectively, the radius of its path would be
(A) $\frac{\text{R}}{4}$
(B) $\frac{\text{R}}{2}$
(C) $2 \text{ R}$...
(a) (i) State Lenz's Law. In a closed circuit, the induced current opposes the change in magnetic flux that produced it as per the law of conservation of energy. Justify. (ii) A metal rod of length 2 m is rotated with a frequency 60 rev/s about an axis passing through its centre and perpendicular to...
An electron moving with a velocity $\vec{v} = (1.0 \times 10^7 \text{ m/s})\hat{i} + (0.5 \times 10^7 \text{ m/s})\hat{j}$ enters a region of uniform magnetic field $\vec{B} = (0.5 \text{ mT})\hat{j}$. Find the radius of the circular path described by it. While rotating; does the electron trace a li...
A coil of area of cross-section $0.5\text{ m}^2$ is placed in a magnetic field acting normally to its plane. The field varies as $B = 0.5t^2 + 2t$, where $B$ is in tesla and $t$ in seconds. The emf induced in the coil at $t = 1\text{s}$ is
(A) $0.5\text{ V}$
(B) $1.0\text{ V}$
(C) $1.5\text{ V}$
(D)...
OR (b) (i) State and explain Ampere's circuital law. (ii) Two long straight parallel wires separated by 20 cm, carry 5 A and 10 A current respectively, in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between them.
An electron moving with a velocity $\vec{v} = (1.0 \times 10^{7} \ \text{m/s})\hat{i} + (0.5 \times 10^{7} \ \text{m/s})\hat{j}$ enters a region of uniform magnetic field $\vec{B} = (0.5 \ \text{mT})\hat{j}$. Find the radius of the circular path described by it. While rotating; does the electron tra...
Two insulated concentric coils, each of radius R, placed at right angles to each other, carry currents I and $\sqrt{3}$ I respectively. The magnitude of the net magnetic field at their common centre will be
(A) $\frac{\mu_0 \text{I}}{\text{R}}$
(B) $\frac{\mu_0 \text{I}}{2\text{R}}$
(C) $\frac{\mu_0...
OR
(b) (i) State and explain Ampere's circuital law.
(ii) Two long straight parallel wires separated by $20\text{ cm}$, carry $5\text{ A}$ and $10\text{ A}$ current respectively, in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between them.
An electron is moving with a velocity $\vec{v} = $3 \times 10^6 \frac{\text{m}}{\text{s}}$\hat{i}$. It enters a region of magnetic field $\vec{B} = (91 \text{mT})\hat{k}$.
(a) Calculate the magnetic force $\vec{F}_B$ acting on electron and the radius of its path.
(b) Trace the path described by it.
The magnetic field due to a current carrying circular coil at a point far off on its axis at a distance 'r' from the centre of the coil is proportional to : (A) $\frac{1}{\text{r}}$ (B) $\frac{1}{\text{r}^2}$ (C) $\frac{1}{\text{r}^{3/2}}$ (D) $\frac{1}{\text{r}^3}$
The magnetic field B within the solenoid of length L having N turns and carrying current I will be : (A) $\mu_0 \text{NIL}$ (B) $\frac{\mu_0 \text{NI}}{\text{L}}$ (C) $\frac{\mu_0 \text{NI}}{4\pi \text{L}}$ (D) $\mu_0 \text{NI}$
An electron is moving along positive x-axis in a magnetic field which is parallel to the positive y-axis. In what direction will the magnetic force be acting on the electron?
(a) Along -x axis
(b) Along -z axis
(c) Along +z axis
(d) Along -y axis
The given figure shows a long straight wire of a circular cross-section (radius a) carrying steady current I. The current I is uniformly distributed across this cross-section. Calculate the magnetic field in the region r < a and r > a.
A charged particle at rest is subjected to an external magnetic field $\vec{B}$. If no other force acts on the particle, then it will :
(a) accelerate along $\vec{B}$
(b) remain at rest
(c) move in a circular path
(d) move with a constant speed along $\vec{B}$
A current carrying loop is placed in a uniform magnetic field. The torque acting on it does not depend upon the : (a) magnetic field (b) current in the loop (c) area of the loop (d) shape of the loop
Two identical coils carrying equal currents are held concentric with their planes perpendicular to each other. The ratio of the magnitude of magnetic field at the centre of one coil to that of the resultant magnetic field at the centre is : (a) $\frac{1}{\sqrt{2}}$ (b) $\sqrt{2}$ (c) $\frac{1}{2}$ (...
(a) (i) Two long parallel straight conductors carrying current $I_1$ and $I_2$ are kept $r$ distance apart in air. Obtain an expression for the force per unit length on one conductor due to the magnetic field produced by the other conductor. Hence, define one ampere. Under what condition will the fo...
(ii) A closely wound circular coil of radius $6\cdot28\text{ cm}$, having $50$ turns carries a steady current of $4\text{ A}$. Find the magnetic field at the centre of the coil. How will the magnitude of the magnetic field be affected if the radius of the coil is halved keeping other factors same ?
OR
(b) (i) A particle of mass $m$ and charge $q$, at the origin moves with a velocity $\vec{v}$ in xy-plane making an angle $\theta$ with x-axis. It is subjected to a uniform magnetic field $\vec{B}$ along x-axis. Justify that the particle will move in a helical path. Hence, obtain expression for th...
(ii) A long straight wire kept horizontally carries a current of $4\text{ A}$ from west to east direction. Find the direction and magnitude of magnetic field $\vec{B}$ at a point $20\text{ cm}$ below the wire.
Assertion (A) : A planar loop of irregular shape carrying current is subjected to a magnetic field acting perpendicular to the plane of the loop. If the wire is flexible, the loop takes a circular shape.
Reason (R) : The force acting on each point of a current carrying loop, in a magnetic field perp...
(a) State Lenz's law. Determine the direction of the induced current when a rectangular conducting loop $abcd$ in $xy$-plane is moved into a region of magnetic field which is directed along $z$-axis.
Assertion (A) : The magnetic field produced by a current carrying solenoid is independent of its length and cross-sectional area.
Reason (R) : The magnetic field inside the solenoid is uniform.
A horizontal straight metallic rod of length $4 \text{ m}$ is held at some height above the surface of Earth, in east-west direction. If it is allowed to fall from rest, find the :
(a) emf induced in the rod $2 \text{ s}$ after it starts falling,
(b) polarity of the emf induced, and
(c) the end of t...
The current $I$ flowing through a conductor of radius $r$ is uniformly distributed across its cross-section. Which of the following graphs represents the variation of magnitude of magnetic field $\vec{B}$ with distance $x$ from the axis of the conductor?
(a) Graph showing B rising linearly to r then...
A planar loop is rotated in a magnetic field about an axis perpendicular to the field. The polarity of induced emf changes once in each :
(a) $1 \text{ revolution}$
(b) $\left(\frac{1}{2}\right) \text{ revolution}$
(c) $\left(\frac{1}{4}\right) \text{ revolution}$
(d) $\left(\frac{3}{4}\right) \...
Assertion (A) : A proton and an alpha particle having same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.
Reason (R) : The centripetal force required to move a charged particle in a circle does not depend on the magnitude of ...
The figure shows a rectangular conductor PQRS with a movable arm PQ, kept in a uniform magnetic field $\vec{B}$ pointing into the page.
(i) PQ is moved towards the right with a velocity $\vec{v}$. Obtain the expression for the emf developed across PQ.
(ii) If $r$ is the resistance of PQRS, find th...
Two long straight parallel conductors carrying steady currents $I_1$ and $I_2$ in the same direction are separated by a distance d. The force exerted by one conductor on unit length of the other is :
(a) $\frac{\mu_0 I_1 I_2}{4\pi d}$, attractive
(b) $\frac{\mu_0 I_1 I_2}{4\pi d}$, repulsive
(c) $\f...
A long solenoid of length L and number of turns N carrying a current I produces a magnetic field B along its axis. If the current in the solenoid is doubled and its number of turns halved, the magnetic field along its axis will be :
(a) $2\text{B}$
(b) $4\text{B}$
(c) $\frac{\text{B}}{2}$
(d) $\text...
The speed of electromagnetic waves in vacuum is :
(a) $\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$
(b) $\sqrt{\mu_0 \varepsilon_0}$
(c) $\mu_0 \varepsilon_0$
(d) $\frac{1}{\mu_0 \varepsilon_0}$
Questions number 16 to 18 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d) as given below.
(a) Both Assertion (A) and Reason (R) are true and Reason...
(a) A metallic rod of length $40 \text{ cm}$ is rotated with a frequency of $300 \text{ rpm}$ about a vertical axis passing through its centre. If a uniform magnetic field of $0 \cdot 2 \text{ T}$ acts vertically downward, find the emf induced between (i) the ends of the rod, and (ii) the centre and...
(a) (i) A charged particle with speed $v_0$ enters a region in which a strong and non-uniform magnetic field exists everywhere. It comes out of the region following a complicated trajectory without suffering any collision in the region. Would its final speed $v$ be equal to its initial speed $v_0$ ?...
(b) (i) Derive an expression for the force acting on a conductor carrying current $I$ in a magnetic field $\vec{B}$.
(ii) A long horizontal conductor carries a current of $30\text{ A}$, in east to west direction. What are the magnitude and direction of the magnetic field due to the current $1.0\text...
Two concentric and coplanar circular loops P and Q have their radii in the ratio $2:3$. Loop Q carries a current $9\text{ A}$ in the anticlockwise direction. For the magnetic field to be zero at the common centre, loop P must carry
(i) $3\text{ A}$ in clockwise direction
(ii) $9\text{ A}$ in clockwi...
Which of the following statement is NOT true about the properties of electromagnetic waves? (i) These waves do not require any material medium for their propagation (ii) Both electric and magnetic field vectors attain the maxima and minima at the same time (iii) The energy in electromagnetic wave is...
A rectangular, a square, a circular and an elliptical loop, all in the $(x-y)$ plane, are moving out of a uniform magnetic field with a constant velocity $\vec{v} = v\hat{i}$. The magnetic field is directed along the negative $z$-axis direction. The induced emf, during the passage of these loops, ou...
A uniform magnetic field gets modified as shown in figure when two specimens A and B are placed in it.
(i) Identify the specimen A and B.
(ii) How is the magnetic susceptibility of specimen A different from that of specimen B?