(a) State Faraday's law of electromagnetic induction.
(b) Derive an expression for the self-inductance of an air-filled long solenoid of length $l$ and cross-sectional area $A$ having $N$ turns.
CBSE CLASS 12 • PHYSICS • CHAPTER 06
Electromagnetic Induction
67 distinct questions across 90 board paper set appearances (2022–2026).
(a) (i) Define self-inductance of a coil. Derive the expression for the energy required to build up a current $I$ in a coil of self-inductance $L$.
(ii) The currents passing through two inductors of self-inductances $10\text{ mH}$ and $20\text{ mH}$ increase with time at the same rate.
Draw graphs s...
Assertion (A) : It is difficult to move a magnet into a coil of large number of turns when the circuit of the coil is closed.
Reason (R) : The direction of induced current in a coil with its circuit closed, due to motion of a magnet, is such that it opposes the cause.
Which of the following quantity/quantities remains same in primary and secondary coils of an ideal transformer ?
Current, Voltage, Power, Magnetic flux
(A) Current only
(B) Voltage only
(C) Power only
(D) Magnetic flux and Power both
Assertion (A) : Lenz's law is a consequence of the law of conservation of energy.
Reason (R) : There is no power loss in an ideal inductor.
(a) (i) With the help of a labelled diagram, explain the working of an ac generator. Obtain the expression for the emf induced at an instant 't'.
(ii) A long, straight horizontal wire X'X is held stationary and carries a current of $3.0\text{ A}$. A square loop MNPS of side $10\text{ cm}$, carrying...
OR (b) (i) A rectangular coil of N turns and area of cross-section A is rotated at a steady angular speed $\omega$ in a uniform magnetic field. Obtain an expression for the emf induced in the coil at any instant of time. (ii) Two coplanar and concentric circular loops $L_1$ and $L_2$ are placed coax...
(a) (i) Define mutual inductance. Write its SI unit. (ii) Derive an expression for the mutual inductance of a system of two long coaxial solenoids of same length $l$, having turns $N_1$ and $N_2$ and of radii $r_1$ and $r_2$ ($> r_1$). OR (b) What are ferromagnetic materials ? Explain ferromagnetism...
The magnetic flux $\phi$ (in Wb) linked with a coil is related to time $t$ (in s) as $\phi = 5\text{ At}^2 + \text{Bt} - 2\text{C}$
The SI units of A and B are respectively
(A) $\text{Wb s}^2$, $\text{Wbs}$
(B) $\text{Wb s}^{-1}$, $\text{Wb}$
(C) $\text{Wbs}^{-2}$, $\text{Wbs}^{-1}$
(D) $\text{Wbs}^...
OR (b) (i) State Lenz's law and explain that it follows the law of conservation of energy. (ii) Write the dimensional formula for self-inductance. The current in a coil changes from $8\cdot0\ \text{A}$ to $2\cdot0\ \text{A}$ in $0\cdot6\ \text{s}$. If an average emf induced in the coil is $50\ \text...
Assertion ($A$) : Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more.
Reason ($R$) : Induced emf produced is directly proportional to the magnetic flux.
(a) State Lenz's law. A rod MN of length L is rotated about an axis passing through its end M perpendicular to its length, with a constant angular velocity $\omega$ in a uniform magnetic field $\vec{B}$ parallel to the axis. Obtain an expression for emf induced between its ends.
OR
(b) Define 'sel...
The dimensions of 'self-inductance' are :
(A) $[\text{M L T}^{-2}\text{ A}^{-2}]$
(B) $[\text{M L}^2\text{ T}^{-1}\text{ A}^{-1}]$
(C) $[\text{M L}^{-1}\text{ T}^{-2}\text{ A}^{-2}]$
(D) $[\text{M L}^2\text{ T}^{-2}\text{ A}^{-2}]$
Assertion (A) : The mutual inductance between two coils is maximum when the coils are wound on each other.
Reason (R) : The flux linkage between two coils is maximum when they are wound on each other.
(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...
The magnetic flux $\phi$ (in $\text{Wb}$) linked with a coil is related to time $t$ (in $\text{s}$) as $\phi = 5 \text{ A} t^2 + \text{B} t - 2\text{C}$
The SI units of A and B are respectively
(A) $\text{Wb s}^2$, $\text{Wbs}$
(B) $\text{Wb s}^{-1}$, $\text{Wb}$
(C) $\text{Wb s}^{-2}$, $\text{Wbs}^...
(a) Define mutual inductance. Give its units. State two factors on which the mutual inductance between a given pair of coils depends. (b) A 1.0 m long solenoid of radius 2 cm having 2000 turns has a secondary coil of 1000 turns wound closely near its mid-point. Find the mutual inductance between the...
(b) (i) State Lenz's law and explain that it follows the law of conservation of energy.
(ii) Write the dimensional formula for self-inductance.
The current in a coil changes from $8\cdot0\text{ A}$ to $2\cdot0\text{ A}$ in $0\cdot6\text{ s}$. If an average emf induced in the coil is $50\text{ V}$, c...
State Faraday's law of electromagnetic induction. Briefly describe two methods for producing induced emf.
The dimensions of the rate of change of magnetic flux are :
(A) $[\text{M L T}^{-3} \text{A}]$
(B) $[\text{M L}^2 \text{T}^{-3} \text{A}^{-1}]$
(C) $[\text{M L}^2 \text{T}^{-2} \text{A}^{-1}]$
(D) $[\text{M L}^2 \text{T}^{-3} \text{A}^{-2}]$
The figure given below shows a square-shaped loop MNOP of side $25 \text{ cm}$ placed horizontally in a uniform magnetic field $\vec{B}$ directed vertically downward. The position of the loop at $t = 0 \text{ s}$ is as shown in figure. The loop is pulled with a constant velocity of $25 \text{ cm/s}$...
Two coils are placed closed to each other. The mutual inductance of the pair of coils depends upon the :
(A) rate at which currents change in the two coils.
(B) relative position and orientation of the coils.
(C) currents in the two coils.
(D) value of voltage induced in one coil due to change in va...
Two coils, one of radius $0.5\text{ cm}$ having $10$ turns and the other of radius $5\text{ cm}$ having $50$ turns are placed coaxially in air such that their centres are coincident. Calculate :
(a) the magnetic flux through the smaller coil if the larger coil carries a current of $3\text{ A}$, and
...
Questions number 13 to 16 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...
Assertion (A) : If $\vec{B}$ be the magnetic field at a small patch of vector area $\vec{\text{dS}}$, then the magnetic flux through the patch will be $\vec{B}.\vec{\text{dS}}$.
Reason (R) : The magnetic flux is a scalar quantity.
Assertion (A) : If $\vec{\text{B}}$ be the magnetic field at a small patch of vector area $\vec{\text{dS}}$, then the magnetic flux through the patch will be $\vec{\text{B}}.\vec{\text{dS}}$.
Reason (R) : The magnetic flux is a scalar quantity.
Assertion (A) : If $\vec{B}$ be the magnetic field at a small patch of vector area $\vec{\mathrm{dS}}$, then the magnetic flux through the patch will be $\vec{B} \cdot \vec{\mathrm{dS}}$.
Reason (R) : The magnetic flux is a scalar quantity.
A current of $5.0\text{ A}$ in one coil is reduced to zero in $10\text{ ms}$ inducing an emf of $9.0\text{ V}$ in the neighbouring coil. The mutual inductance of the two coils is :
(A) $18\text{ mH}$
(B) $1.8\text{ mH}$
(C) $0.18\text{ mH}$
(D) $0.18\text{ H}$
(a) State Faraday's Law of electromagnetic induction.
(b) A rectangular coil of area A having number of turns N is rotated with angular velocity $\omega$ in a uniform magnetic field $\vec{B}$ directly perpendicular to the plane of the coil. Obtain an expression for the instantaneous value of emf ind...
(b) (i) What will be the directions of induced current when the loop enters the field and when it leaves the field ?
(II) Draw the plots showing the variation of magnetic flux $\phi$ linked with the loop with time $t$ and variation of induced emf $E$ with time $t$. Mark the relevant values of $E$, $...
When current in a coil changes at a steady rate from $8\text{ A}$ to $6\text{ A}$ in $4\text{ ms}$, an emf of $1.5\text{ V}$ is induced in it. The value of self-inductance of the coil is :
(A) $6\text{ mH}$
(B) $12\text{ mH}$
(C) $3\text{ mH}$
(D) $9\text{ mH}$
State Lenz's law and explain how this law is a consequence of conservation of energy principle.
The magnetic flux linked with a closed coil (in $ ext{Wb}$) varies with time $t$ (in $ ext{s}$) as $\phi = 5t^2 + 4t - 2$. If the resistance of the circuit is $14\text{ }\Omega$, the magnitude of induced current in the coil at $t = 1\text{ s}$ will be :
(A) $0.5\text{ A}$
(B) $1.0\text{ A}$
(C) $1.5...
(a) Obtain an expression for the self-inductance of a long solenoid of length '$l$', cross-sectional area 'A' and having '$N$' turns.
(b) The figure shows the plot of magnitude of induced emf ($\varepsilon$) versus the rate of change of current in two coils '1' and '2'. Which coil has greater value...
(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...
The magnetic flux linked with a coil changes with time $t$ as $\phi = (8t^2 + 5t + 7)$, where $t$ is in seconds and $\phi$ is in $\text{Wb}$. The value of emf induced in the coil at $t = 4\text{ s}$ is :
(A) $32\text{ V}$
(B) $37\text{ V}$
(C) $64\text{ V}$
(D) $69\text{ V}$
(a) State Lenz's law. A rod $\text{MN}$ of length $L$ is rotated about an axis passing through its end $\text{M}$ perpendicular to its length, with a constant angular velocity $\omega$ in a uniform magnetic field $\vec{B}$ parallel to the axis. Obtain an expression for emf induced between its ends.\...
(a) State Faraday's law of electromagnetic induction and explain the role of negative sign in its expression.
(b) Explain, with an example, that Lenz's law is consistent with the law of conservation of energy.
The dimensions of 'self-inductance' are :
(A) $[M\ L\ T^{-2}\ A^{-2}]$
(B) $[M\ L^2\ T^{-1}\ A^{-1}]$
(C) $[M\ L^{-1}\ T^{-2}\ A^{-2}]$
(D) $[M\ L^2\ T^{-2}\ A^{-2}]$
The stopping potential $V_0$ measured in a photoelectric experiment for a metal surface is plotted against frequency $\nu$ of the incident radiation. Let m be the slope of the straight line so obtained. Then the value of charge of an electron is given by (h is the Planck's constant.)
(A) mh
(B) $\fr...
(a) State Lenz's law.
(b) In the given figure :
(i) Identify the machine.
(ii) Name the parts $\text{P}$ and $\text{Q}$ and $\text{R}$ of the machine.
(iii) Give the polarities of the magnetic poles.
(iv) Write the two ways of increasing the output voltage.
The magnetic flux through a loop changes from $3.6 \text{ Wb}$ to $1.6 \text{ Wb}$ in $0.4 \text{ s}$. The magnitude of the induced emf in the loop is —
(A) $5 \text{ V}$
(B) $2.5 \text{ V}$
(C) $1.5 \text{ V}$
(D) $0.5 \text{ V}$
Assertion (A): On increasing the current sensitivity of a galvanometer by increasing the number of turns may not necessarily increase its voltage sensitivity.
Reason(R): The resistance of the coil of the galvanometer increases on increasing the number of turns.
A series LCR circuit ($L = 2\text{ mH}$, $C = 0\cdot2\text{ }\mu\text{F}$ and $R = 30\text{ }\Omega$) is connected to an ac source of variable frequency. The impedance of this circuit will be minimum at a frequency of:
(A) $\frac{10^5}{4\pi}\text{ Hz}$
(B) $\frac{10^5}{2\pi}\text{ Hz}$
(C) $\frac{10...
(a) Define coefficient of self-inductance.
(b) A solenoid has length $12\text{ cm}$, area of cross-section $24\text{ cm}^2$ and $1500$ turns. Calculate the self-inductance of the solenoid.
A coil of resistance $20 \; \Omega$ and self-inductance $10 \; \text{mH}$ is connected to an ac source of frequency $1000/\pi \; \text{Hz}$. The phase difference between current in the circuit and the source voltage is :
(A) $30^{\circ}$ (B) $60^{\circ}$ (C) $75^{\circ}$ (D) $45^{\circ}$
An inductor of resistance $5 \ \Omega$ and self-inductance $25 \ \text{mH}$ is connected across an ac source of angular frequency $200 \ \text{rad s}^{-1}$. The phase angle between the voltage and the current is :
(A) $30^{\circ}$
(B) $45^{\circ}$
(C) $60^{\circ}$
(D) $90^{\circ}$
A current of $1$ $\text{A}$ flows through an inductor connected to a $200$ $\text{V}$ $\text{dc}$ source. When it is connected to $200$ $\text{V}$, $50$ $\text{Hz}$ source, only $0.5$ $\text{A}$ current flows. Calculate the self-inductance of the inductor.
The current in a coil of $15 \text{ mH}$ increases uniformly from zero to $4 \text{ A}$ in $0.004 \text{ s}$. The emf induced in the coil will be :
(A) $22.5 \text{ V}$
(B) $17.5 \text{ V}$
(C) $15.0 \text{ V}$
(D) $12.5 \text{ V}$
The mutual inductance of two coils $C_1$ and $C_2$ is $20 \text{ mH}$. In coil $C_1$, the current changes from $4 \text{ A}$ to zero in $0\cdot 2 \text{ s}$. If the resistance of coil $C_2$ is $4 \text{ } \Omega$, then the charge that flows through it per second will be :
(A) $4\cdot 0 \text{ C}$
(B...
Prove that induced charge depends on the net change in the magnetic flux and not on the time interval of the flux change.
A circular loop A of radius R carries a current I. Another circular loop B of radius $r = \frac{\text{R}}{20}$ is placed concentrically in the plane of A. The magnetic flux linked with loop B is proportional to
(A) R
(B) $\sqrt{\text{R}}$
(C) $\text{R}^{\frac{3}{2}}$
(D) $\text{R}^2$
A circular loop A of radius R carries a current I. Another circular loop B of radius $r = \frac{R}{20}$ is placed concentrically in the plane of A. The magnetic flux linked with loop B is proportional to (A) R (B) $\sqrt{R}$ (C) $R^{\frac{3}{2}}$ (D) $R^2$
A circular loop A of radius $\text{R}$ carries a current $\text{I}$. Another circular loop B of radius $\text{r} = \left(\frac{\text{R}}{20}\right)$ is placed concentrically in the plane of A. The magnetic flux linked with loop B is proportional to
(A) $\text{R}$
(B) $\sqrt{\text{R}}$
(C) $\text{R}^...
Two coils are placed near each other. When the current in one coil is changed at the rate of $5 \text{ A/s}$, an emf of $2 \text{ mV}$ is induced in the other. The mutual inductance of the two coils is
(A) $0.4 \text{ mH}$
(B) $2.5 \text{ mH}$
(C) $10 \text{ mH}$
(D) $2.5 \text{ H}$
The mutual inductance of two coils, in a given orientation is $50 \; \text{mH}$. If the current in one of the coils changes as $\text{i} = 1.0 \sin \left$ 100 \pi \text{t} + \frac{\pi}{3} \right$ \text{A}$, the peak value of emf (in volt) induced in the other coil will be
(A) $\frac{\pi}{5}$
(B) $5\...
The magnetic flux $\phi$ (in Wb) through a closed loop of resistance $3\cdot0 \Omega$ varies with time t (s) as $\phi = 6t^2 + 3\cdot0t + 5$. The value of the induced current in the loop at t = $1\cdot0$ s is :
(A) $15\cdot0$ A
(B) $3\cdot0$ A
(C) $4\cdot0$ A
(D) $5\cdot0$ A
(a) (i) Define the term 'self-inductance' of a coil. Obtain an expression for self-inductance of a solenoid of area of cross-section $A$, length $L$ and having $n$ turns per unit length. (ii) The current flowing in a coil of inductance $50$ $ ext{mH}$ is reduced from $10$ $ ext{A}$ to $0$ in $20$ $ ...
a. Define mutual inductance and write its SI unit.
Two circular loops, one of small radius $r$ and other of larger radius $R$, such that $R >> r$, are placed coaxially with centres coinciding. Obtain the mutual inductance of the arrangement.
The magnetic flux (in SI units) through a coil varies with time as $\phi = 3t^2 + 4t + 7$. The ratio of emf induced in the coil at $t = 2\text{ s}$ to that at $t = 1\text{ s}$ will be :
(a) 2
(b) 0.8
(c) 1.6
(d) 4
Which of the following statements is not correct? (a) Lenz's law is the consequence of the law of conservation of energy. (b) The magnitude of induced emf in a coil is directly proportional to the rate of change of magnetic flux. (c) Inserting an iron core in a coil decreases its self-inductance. (d...
Define the term 'self-inductance' of a coil. Obtain the expression for the self-inductance of a long solenoid of length $l$, cross-sectional area A and having N turns.
A metal detector is based on :
(a) Self-induction
(b) Mutual induction
(c) Electrical resonance
(d) Power transmission
Answer the following, giving reasons : (a) Induced emf does not always produce induced current. (b) The motion of a copper plate is damped when it is allowed to oscillate between pole pieces of a strong magnet. (c) No power is consumed in an ac circuit containing a pure inductor.
State Lenz's law. Show that it is consistent with the principle of conservation of energy.
A closely wound coil having 100 turns carries a current of 2 A. If the magnetic flux linked with coil is $\pi^2 \times 10^{-5}$ Wb, find the radius of the coil.