(a) Using Gauss's law, deduce an expression for electric field at a point due to a uniformly charged infinite plane thin sheet.
(b) Two large thin plane sheets, each having surface charge density $\sigma$, are held close and parallel to each other in air. What is the net electric field at a point (i...
CBSE CLASS 12 • PHYSICS • CHAPTER 01
Electric Charges and Fields
237 distinct questions across 304 board paper set appearances (2022–2026).
(a) (i) In the figure, OA and OB show the variation of electric potential V at a point due to two point charges $Q_1$ and $Q_2$ with $\frac{1}{r}$ respectively. Here r represents the distance of the point from the two point charges. (I) Identify the nature of the two charges $Q_1$ and $Q_2$. (II) Wh...
The ratio of amplitude of electric field to the amplitude of the magnetic field associated with an electromagnetic wave propagating in glass ($n = 1.5$) is :
(A) $3 \times 10^8 \text{ ms}^{-1}$
(B) $2 \times 10^8 \text{ ms}^{-1}$
(C) $3.3 \times 10^{-9} \text{ ms}^{-1}$
(D) $5 \times 10^{-9} \text{ ...
The electric potential ($V$) and electric field ($E$) are closely related concepts in electrostatics. The electric field is a vector quantity that represents the force per unit charge at a given point in space, whereas electric potential is a scalar quantity that represents the potential energy per ...
Assume that the surface charge density of the Earth is $1$ electron charge/$\text{m}^2$. The potential of the Earth's surface (radius $6400\text{ km}$) will be :
(A) $- 0\cdot 12\text{ V}$
(B) $- 0\cdot 21\text{ V}$
(C) $+ 2\cdot 1\text{ V}$
(D) $+ 1\cdot 2\text{ V}$
A conducting sphere of radius R has a charge Q on it. Which of the following graphs correctly represents the value of electric field E in the range $0 \le x < \infty$, where x is the distance of the point from the centre of the sphere ?
(A) graph showing E constant for $x < R$ and decreasing for $x ...
In an electromagnetic wave, the electric field ($\vec{E}$) and the magnetic field ($\vec{B}$) oscillate along x-axis and y-axis respectively. The wave is propagating along :
(A) z-axis
(B) $-z$-axis
(C) x-axis
(D) $-y$-axis
A current of $\left$\frac{10}{\pi}\right$\text{ A}$ is maintained in a circular loop of radius $14\text{ cm}$. The value of dipole moment associated with the loop is :
(A) $0.019\text{ Am}^2$
(B) $0.14\text{ Am}^2$
(C) $0.196\text{ Am}^2$
(D) $0.615\text{ Am}^2$
A charge $Q$ is enclosed by a spherical Gaussian surface of radius $R$. If the radius is doubled, then the total electric flux through the surface :
(A) becomes four times
(B) remains the same
(C) becomes half
(D) becomes twice
A thin plastic rod is bent into a circular ring of radius $R$. It is uniformly charged with charge density $\lambda$. The magnitude of the electric field at its centre is :
(A) $\frac{\lambda}{2\varepsilon_0 R}$
(B) Zero
(C) $\frac{\lambda}{4\pi\varepsilon_0 R}$
(D) $\frac{\lambda}{4\varepsilon_0 R}...
Which one of the following statements is correct? Electric field due to static charges is (A) conservative and field lines do not form closed loops. (B) conservative and field lines form closed loops. (C) non-conservative and field lines do not form closed loops. (D) non-conservative and field lines...
A constant electric field is to be maintained between the two plates of a capacitor whose separation $d$ changes with time. Which of the graphs correctly depict the potential difference ($V$) to be applied between the plates as a function of separation between the plates ($d$) to maintain the consta...
(a) (i) A small conducting sphere A of radius $r$ charged to a potential $V$, is enclosed by a spherical conducting shell B of radius $R$. If A and B are connected by a thin wire, calculate the final potential on sphere A and shell B.
(ii) Write two characteristics of equipotential surfaces. A unifo...
(a) (i) Obtain an expression for the electric potential due to a small dipole of dipole moment $\vec{p}$, at a point $\vec{r}$ from its centre, for much larger distances compared to the size of the dipole. (ii) Three point charges q, 2q and nq are placed at the vertices of an equilateral triangle. I...
(a) The radius of a conducting wire AB uniformly decreases from its one end A to another end B. It is connected across a battery. How will (i) electric field, (ii) current density, and (iii) mobility of electrons change from end A to end B ? Justify your answer in each case. OR (b) Two large plane s...
An electron is revolving with speed v around the proton in a hydrogen atom, in a circular orbit of radius r. The magnitude of magnetic dipole moment of the electron is :
(A) $4\ evr$
(B) $2\ evr$
(C) $\frac{1}{2}\ evr$
(D) $\frac{1}{4}\ evr$
(i) For which pair of the plates is the electric field $\vec{E}$ along $\hat{i}$ ?
(A) I
(B) II
(C) III
(D) IV
(a) (i) (1) What is meant by current sensitivity of a galvanometer? Mention the factors on which it depends. (2) A galvanometer of resistance G is converted into a voltmeter of range (0 - V) by using a resistance R. Find the resistance, in terms of R and G, required to convert it into a voltmeter of...
The phase difference between electric field $\vec{E}$ and magnetic field $\vec{B}$ in an electromagnetic wave propagating along z-axis is
(A) zero
(B) $\pi$
(C) $\frac{\pi}{2}$
(D) $\frac{\pi}{4}$
Assertion (A) : Equal amount of positive and negative charges are distributed uniformly on two halves of a thin circular ring as shown in figure. The resultant electric field at the centre O of the ring is along OC.
Reason (R) : It is so because the net potential at O is not zero.
(a) (i) Draw equipotential surfaces for an electric dipole.
(ii) Two point charges $q_1$ and $q_2$ are located at $\vec{r}_1$ and $\vec{r}_2$ respectively in an external electric field $\vec{E}$. Obtain an expression for the potential energy of the system.
(iii) The dipole moment of a molecule is $1...
(a) The electric field of an electromagnetic wave passing through vacuum is represented as $E_x = E_0 \sin $kz - \omega t$$. Identify the parameter which is related to the (i) wavelength, and (ii) the frequency of the wave in the above equation.
(b) Write two properties of a medium that determine th...
(a) An electric dipole consists of two point charges $q$ and $-q$ separated by a distance $2a$. Derive an expression for the electric field $\vec{\text{E}}$ due to this dipole at a point distant $r$ from the centre of the dipole on the equatorial plane. Write the expression for the electric field at...
An electric dipole consists of two point charges $+1 \text{ }\mu\text{C}$ and $-1 \text{ }\mu\text{C}$, held $10 \text{ cm}$ apart. It is subjected to a uniform electric field of $100 \text{ N/C}$. Calculate the amount of work done in turning the dipole from its position of stable equilibrium to the...
The electric field $\vec{E}$ in the region between the plates is :
(A) $\left$2 \times 10^{2} \frac{\text{V}}{\text{m}}\right$ \hat{k}$
(B) $-\left$2 \times 10^{2} \frac{\text{V}}{\text{m}}\right$ \hat{k}$
(C) $\left$2 \times 10^{4} \frac{\text{V}}{\text{m}}\right$ \hat{k}$
(D) $-\left$2 \times 10^{...
(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} = \ve...
(a) (i) Two point charges $+q$ and $-q$ are held at $(a, 0)$ and $(-a, 0)$ in x-y plane. Obtain an expression for the net electric field due to the charges at a point $(0, y)$. Hence, find electric field at a far off point ($y \gg a$).
(ii) Three point charges of $-2\text{ nC}$, $-1\text{ nC}$, and ...
The electric field at a point in a region is given by $\vec{E} = \alpha \frac{\vec{r}}{|\vec{r}|^3}$, where $\alpha$ is a constant and $r$ is the distance of the point from the origin. The magnitude of potential of the point is :
(A) $\frac{\alpha}{r}$
(B) $\frac{\alpha r^2}{2}$
(C) $\frac{\alpha}{2...
The dimensions of $(\mu\varepsilon)^{-1}$, where $\varepsilon$ is permittivity and $\mu$ is permeability of a medium, are :
(A) $[\text{M}^0 \text{L}^1 \text{T}^{-1}]$
(B) $[\text{M}^0 \text{L}^2 \text{T}^{-2}]$
(C) $[\text{M}^1 \text{L}^2 \text{T}^{-2}]$
(D) $[\text{M}^1 \text{L}^{-1} \text{T}^1]$
(b) (i) Current $I$ ($= 1\text{ A}$) is passing through a copper rod ($n = 8\cdot5 \times 10^{28}\text{ m}^{-3}$) of varying cross-sections as shown in the figure. The areas of cross-section at points A and B along its length are $1\cdot0 \times 10^{-7}\text{ m}^2$ and $2\cdot0 \times 10^{-7}\text{ ...
(a) Two small solid metal balls A and B of radii $R$ and $2R$ having charge densities $2\sigma$ and $3\sigma$ respectively are kept far apart. Find the charge densities on A and B after they are connected by a conducting wire.
OR
(b) Two infinitely long straight wires '1' and '2' are placed $d$ dist...
(a) (i) The electric field in a region is given by $\vec{E} = 40x\hat{i}\text{ N/C}$. Find the amount of work done in taking a unit positive charge from a point $(0, 3\text{m})$ to the point $(5\text{m}, 0)$.
(ii) A charge $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$ ($...
A steady current flows in a copper wire of non-uniform cross-section. Consider the following three physical quantities :
I. Electric field
II. Current density
III. Drift speed
Then at the different points along the wire :
(A) II and III change, but I is constant.
(B) I and II change, but III i...
Three parallel plates are placed above each other with equal displacement $\vec{d}$ between neighbouring plates. The electric field between the first pair of the plates is $\vec{E}_1$ and the electric field between the second pair of the plates is $\vec{E}_2$. The potential difference between the th...
(a) (i) Derive an expression for potential energy of an electric dipole $\vec{p}$ in an external uniform electric field $\vec{E}$. When is the potential energy of the dipole (1) maximum, and (2) minimum ?
(ii) An electric dipole consists of point charges $-1.0\text{ pC}$ and $+1.0\text{ pC}$ located...
OR (b) (i) State Gauss's Law in electrostatics. Apply this to obtain the electric field $\vec{E}$ at a point near a uniformly charged infinite plane sheet. (ii) Two long straight wires 1 and 2 are kept as shown in the figure. The linear charge density of the two wires are $\lambda_1 = 10 \ \mu\text{...
Two identical electric dipoles, each consisting of charges $-q$ and $+q$ separated by distance d, are arranged in x-y plane such that their negative charges lie at the origin O and positive charges lie at points (d, 0) and (0, d) respectively. The net dipole moment of the system is :
(A) $-qd$\hat{...
Dipoles, whether electric or magnetic, are characterised by their dipole moments, which are vector quantities. Two equal and opposite charges separated by a small distance constitute an electric dipole, while a current carrying loop behaves as a magnetic dipole. Electric dipoles create electric fiel...
$E_1$ and $E_2$ are magnitudes of electric field due to a dipole, consisting of charges $-q$ and $+q$ separated by distance $2a$, at points $r (>> a)$ (1) on its axis, and (2) on equatorial plane, respectively. Then $\left(\frac{E_1}{E_2}\right)$ is :
(A) $\frac{1}{4}$
(B) $\frac{1}{2}$
(C) 2
(D) 4
An electric dipole of dipole moment $5.0 \times 10^{-8} \text{ Cm}$ is placed in a region where an electric field of magnitude $1.0 \times 10^3 \text{ N/C}$ acts at a given instant. At that instant the electric field $\vec{E}$ is inclined at an angle of $30^\circ$ to dipole moment $\vec{P}$. The mag...
Let $E_1$, $E_2$, $E_3$ and $E_4$ be the magnitudes of the electric field between the pairs of plates, I, II, III and IV respectively. Then: (A) $E_1 > E_2 > E_3 > E_4$ (B) $E_3 > E_4 > E_1 > E_2$ (C) $E_4 > E_3 > E_2 > E_1$ (D) $E_2 > E_3 > E_4 > E_1$
OR (b) Three point charges, $1 \text{ pC}$ each, are kept at the vertices of an equilateral triangle of side $10 \text{ cm}$. Find the net electric field at the centroid of triangle.
Which of the following statements about dielectrics is correct?
(A) A polar dielectric has a net dipole moment in absence of an external electric field which gets modified due to the induced dipoles.
(B) The net dipole moments of induced dipoles is along the direction of the applied electric field.
...
When a dielectric slab is inserted between the plates of an isolated charged capacitor, the energy stored in it:
(A) increases and the electric field inside it also increases.
(B) decreases and the electric field also decreases.
(C) decreases and the electric field increases.
(D) increases and the e...
(b) (i) A thin spherical shell of radius R has a uniform surface charge density $\sigma$. Using Gauss' law, deduce an expression for electric field (i) outside and (ii) inside the shell.
(ii) Two long straight thin wires AB and CD have linear charge densities $10 \text{ } \mu\text{C/m}$ and $-20 \te...
In a region, the electric potential varies as $V = 10 - 50x$, where V is in volts and $x$ in meters. The electric field in the region is :
(A) $10\text{ N/C along } +x$
(B) $10\text{ N/C along } -x$
(C) $50\text{ N/C along } +x$
(D) $50\text{ N/C along } -x$
(a) An electric dipole consists of two point charges $q$ and $-q$ separated by a distance $2a$. Derive an expression for the electric field $\vec{E}$ due to this dipole at a point distant $r$ from the centre of the dipole on the equatorial plane. Write the expression for the electric field at a far ...
In a region electric field is given by $\vec{E} = 4\hat{x}\text{ N/C}$. The potential difference between points A ($x = 1\text{ m}$) and B ($x = 3\text{ m}$), ($V_{\text{A}} - V_{\text{B}}$) is
(A) $-16\text{ V}$
(B) $16\text{ V}$
(C) $-8\text{ V}$
(D) $8\text{ V}$
The electric potential for various points in $x\text{-}y$ plane is given by $V = 1.0\, x^2 - 2.0\, y^2$, where V is in volts and $x$, $y$ are in metres. The angle that the electric field at point $(2.0\text{ m}, 1.0\text{ m})$ makes with the positive $x$-axis is ---
(A) $45^{\circ}$
(B) $90^{\circ...
A current of $1.5\text{ A}$ is maintained in a copper wire of length $1\text{ m}$ with area of cross-section $1.7 \times 10^{-7}\text{ m}^2$. The magnitude of electric field in the wire is [$\rho_{\text{Cu}} = 1.7 \times 10^{-8}\text{ }\Omega\text{ m}$]
(A) $0.15\,\frac{\text{V}}{\text{m}}$
(B) $0...
Three point charges $2q$, $-2q$ and $q$ are kept at the vertices of an equilateral triangle of side $l$. The potential energy of the system is
(A) zero
(B) $\frac{-2q^2}{\pi\varepsilon_0 l}$
(C) $\frac{q^2}{2\pi\varepsilon_0 l}$
(D) $\frac{-q^2}{\pi\varepsilon_0 l}$
An electromagnetic wave is propagating along x-axis. At any instant, the phase difference (in radian) between the electric field $(\vec{E})$ and the magnetic field $(\vec{B})$ associated with the wave is
(A) zero
(B) $\frac{\pi}{4}$
(C) $\frac{\pi}{2}$
(D) $\pi$
(a) An electric field $\vec{\text{E}} = \text{E}_0\hat{\text{i}}$ exists in a region of space. Draw three equipotential surfaces in the region.
(b) Two point charges $-q$ and $+q$ are located at points $(-a,\text{ }0,\text{ }0)$ and $(a,\text{ }0,\text{ }0)$ respectively. Find the electrostatic pot...
Three point charges $+q$, $-2q$ and $+q$ are placed along $x$-axis at points $x = -1 ext{ m}$, $x = 0 ext{ m}$ and $x = 2 ext{ m}$ respectively. The potential energy of the system is
(A) $-\frac{q^2}{\pi\varepsilon_0}$
(B) $-\frac{2q^2}{3\pi\varepsilon_0}$
(C) $\frac{q^2}{4\pi\varepsilon_0}$
(D) $\f...
(i) Draw electric field lines and equipotential surfaces for a system of two equal and opposite point charges separated by some distance.
(ii) Why electric field $\vec{\text{E}}$ at a point on an equipotential surface must be perpendicular to the surface at that point?
The electric field and the magnetic field components of an electromagnetic wave travelling in vacuum are represented as
$E = m \sin(\alpha z - \beta t)$
$B = n \sin(\alpha z - \beta t)$
where $m$, $n$, $\alpha$ and $\beta$ are constants characterising the wave. Then
(A) $\frac{m}{n} = c, \frac{\beta...
A point charge of $5\text{ }\mu\text{C}$ is located at $(1\text{ cm}, 1\text{ cm})$ in $x$-$y$ plane. A second charge of $6\text{ }\mu\text{C}$ is brought from infinity to point $(-3\text{ cm}, 4\text{ cm})$. The work done in the process is
(A) $0.54\text{ J}$
(B) $5.4\text{ J}$
(C) $-0.54\text{ J}$...
(a) Draw electric field lines and equipotential surfaces for a system of two equal positive charges separated by some distance.
(b) Using the drawing in (a) above, explain that electric field need not be a constant over each point of an equipotential surface.
Which of the following is not correct about the electrostatic force between two charges ?
(A) The magnitude of the force is directly proportional to the magnitudes of the two charges.
(B) It is inversely proportional to the square of the distance between the two charges.
(C) It depends on the permit...
The value of potential barrier across a depletion region $2\cdot 0$ $\mu\text{m}$ wide is $0\cdot 4$ V. The value of the electric field in this region is :
(A) $5 \times 10^{6}$ $\text{Vm}^{-1}$
(B) $5 \times 10^{-6}$ $\text{Vm}^{-1}$
(C) $0\cdot 8 \times 10^{6}$ $\text{Vm}^{-1}$
(D) $2\cdot 0 \time...
(a) An electric dipole consists of two point charges $+ q$ and $- q$ separated by a distance $2a$. The dipole is centered at the origin and is placed along the x-axis. Obtain : (i) the electric potential at a point which is at a distance x from the centre of the dipole when (I) $x > a$, and (II) $x ...
Electric potential and electric field are related to each other. One can be derived from the other. The electrostatic potential energy is the energy possessed by a system of point charges by virtue of their positions. When point charges are at infinite separation, the potential energy of such a syst...
The electrostatic potential energy (U) of a system of two point charges $q_1$ and $q_2$ with their position vectors $\vec{r}_1$ and $\vec{r}_2$ is : $\left( k = \frac{1}{4\pi\varepsilon_0} \right)$
(A) $k \left[ \frac{q_1}{r_1} + \frac{q_2}{r_2} \right]$
(B) $k \frac{(q_1 + q_2)}{r_{12}}$
(C) $k ...
If the distance between two point charges is halved, the electrostatic potential energy of the system will :
(A) become double
(B) become half
(C) become one-fourth
(D) remain the same
Two point charges $4 \mu\text{C}$ and $-2 \mu\text{C}$ are $1 \text{m}$ apart in air. The least distance of the point from $4 \mu\text{C}$ charge, where the potential is zero is :
(A) $\frac{1}{3} \text{m}$
(B) $\frac{2}{3} \text{m}$
(C) $\frac{1}{2} \text{m}$
(D) $1 \text{m}$
(a) (i) An electric field $\vec{E}$ is maintained in a conductor of length $L$ and area of cross-section $A$. Show that the electrons drift with an average velocity $\vec{v}_d = \frac{-e\vec{E}}{m} \tau$. Here symbols have their usual meanings.
(ii) Electrons in metals drift due to force experienced...
When an electric dipole of charges $\pm q$ and dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$ making an angle $\theta$ with the electric field $\vec{E}$, then two charges experience equal and opposite forces $+q\vec{E}$ and $-q\vec{E}$. These equal and opposite forces cancel...
The magnitude of electric field at a certain distance from a dipole on its axis is $E_1$ and at the same distance on the equatorial plane of the dipole is $E_2$. Then $\left$ \frac{E_1}{E_2} \right$$ is
(A) $\frac{1}{2}$
(B) $2$
(C) $\frac{1}{4}$
(D) $4$
An electric dipole having dipole moment of $4 \times 10^{-9}\text{ Cm}$ is placed in a uniform electric field of $5 \times 10^4\text{ N/C}$. If the angle between the dipole moment and the electric field is $30^\circ$ then the value of potential energy of the dipole is –
(A) $3.23 \times 10^{-4}\text...
The dimensional formula of dipole moment is –
(A) $[\text{L}^2\text{T}^2\text{A}^{-2}]$
(B) $[ ext{M}^2\text{L}^2\text{TA}^2]$
(C) $[ ext{LTA}^2]$
(D) $[ ext{LTA}]$
An electric dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$. The torque exerted by the field on the dipole at that instant is –
(A) parallel to both $\vec{E}$ & $\vec{p}$.
(B) perpendicular to both $\vec{E}$ & $\vec{p}$.
(C) parallel to $\vec{E}$ and perpendicular t...
A particle of mass m and charge q starts from rest and moves in an electric field $\vec{E} = E_0 \hat{i}$. After travelling a distance x in the field along x-axis, the kinetic energy of the particle will be : (A) $q E_0 x^2$ (B) $q E_0 x$ (C) $q^2 E_0 x$ (D) $q^2 E_0^2 x$
(ii) A small hollow conducting sphere of radius $r_1$ is given a charge $Q$. It is surrounded by a concentric conducting spherical shell of inner radius $r_2$ and outer radius $r_3$, having charge $-3q$. If a point charge $2q$ were kept at the centre, find : (I) the electric flux through a concentri...
An electric dipole $\vec{P} = 2qa \hat{i}$ is placed in x-y plane, centred at the origin. Let $E_1$ and $E_2$ be the magnitudes of electric field at a point distant r (>> a) from its centre, along its axis and on its equatorial plane, respectively. Then the value of $\left$ \frac{E_1}{E_2} \right$$ ...
(ii) Two point charges $-2\text{ }\mu\text{C}$ and $5\text{ }\mu\text{C}$ are placed at $(-30\text{ cm}, 0)$ and $(30\text{ cm}, 0)$ respectively in an external electric field $\vec{E} = \frac{\text{A}}{\text{x}^2} \hat{i}$, where $\text{A} = 9 \times 10^5 \text{ Nm}^2 \text{C}^{-1}$. Find the elect...
OR (b) (i) Two infinitely long straight wires having linear charge densities $-\lambda$ and $3\lambda$ are held vertically parallel to each other, distance r apart in free space. Find the nature and magnitude of the force/length exerted by one wire on the other. (ii) A small hollow conducting sphere...
A square loop of side L lies in the x-y plane in a magnetic field $\vec{\text{B}} = \text{B}_0$2\hat{\text{i}} + 3\hat{\text{j}} + 4\hat{\text{k}}$$, where $\text{B}_0$ is a constant. The magnetic flux through the loop is : (A) $\sqrt{29} \; \text{B}_0 \text{L}^2$ (B) $4 \; \text{B}_0 \text{L}^2$ (C...
An electric dipole with dipole moment $\vec{P} = (2.54 \times 10^{-28} \text{ C.m}) (2.00\hat{i} + 3.00\hat{j})$ is placed in an electric field $\vec{E} = $1000 \frac{\text{N}}{\text{C}}$\hat{i}$. An external agent turns the dipole until its electric dipole moment is $\vec{P} = (2.54 \times 10^{-28}...
(ii) Two point charges $-2 \,\mu\text{C}$ and $5 \,\mu\text{C}$ are placed at $(-30 \text{ cm}, 0)$ and $(30 \text{ cm}, 0)$ respectively in an external electric field $\vec{\text{E}} = \frac{\text{A}}{\text{x}^2} \hat{\text{i}}$, where $\text{A} = 9 \times 10^5 \text{ Nm}^2 \text{C}^{-1}$. Find the...
(b) (i) Two infinitely long straight wires having linear charge densities $-\lambda$ and $3\lambda$ are held vertically parallel to each other, distance $\text{r}$ apart in free space. Find the nature and magnitude of the force/length exerted by one wire on the other.
(ii) A small hollow conducting ...
An electric dipole consists of two point charges $+1 \mu \text{C}$ and $-1 \mu \text{C}$, held $10 \text{ cm}$ apart. It is subjected to a uniform electric field of $100 \text{ N/C}$. Calculate the amount of work done in turning the dipole from its position of stable equilibrium to the position of u...
Which of the following statements is true about mobility of charge carriers in a metal ?
(A) Mobility increases with increase in applied electric field.
(B) Mobility decreases with increase in temperature.
(C) Mobility is independent of the mass of the charge carrier.
(D) Mobility increases with inc...
Two point charges $-Q$ and $Q$ are located at points $(d, 0)$ and $(0, d)$ respectively, in x-y plane. The electric field $\vec{E}$ at the origin will be :
(A) $\frac{1}{4\pi\varepsilon_0} \frac{\sqrt{2} Q}{d^2}$\hat{i} - \hat{j}$$
(B) $\frac{1}{4\pi\varepsilon_0} \frac{\sqrt{2} Q}{d^2}$-\hat{i} - \...
An electron is moving with velocity $v_0 \hat{i}$. If a uniform electric field $\vec{E} = E_0 \hat{j}$ is set up in the region, the electron will :
(A) describe a circular path
(B) describe a helical path
(C) describe a parabolic path
(D) continue moving without any deviation
A charged particle of mass $m$ having kinetic energy $K$ passes undeflected through a region with electric field $\vec{E}$ and magnetic field $\vec{B}$ acting perpendicular to each other. The mass $m$ of the particle will be :
(A) $\frac{KB^2}{2E^2}$
(B) $\frac{2KB^2}{E^2}$
(C) $\frac{2KE^2}{B^2}$
(...
A pair of square conducting plates having sides of length $0.05\text{ m}$ are arranged parallel to each other in $x\text{-}y$ plane. They are $0.01\text{ m}$ apart along $z$-axis and are connected to a $200\text{ V}$ power supply as shown in the figure. An electron enters with a speed of $3 \times 1...
The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be :
(A) $\frac{q}{4\pi\varepsilon_0 l^2}$ pointing along MA
(B) $\frac{q}{\pi\varepsilon_0 l^2}$ pointing along AM
(C) $\frac{q}{2\p...
Two point charges $q_1 = 2.5 \times 10^{-7}\text{ C}$ and $q_2 = -2.5 \times 10^{-7}\text{ C}$ are located at points $(0, 0, -15\text{ cm})$ and $(0, 0, 15\text{ cm})$ respectively. Find :
(a) the electric dipole moment of the system, and
(b) the magnitude and direction of electric field at the orig...
(a) Two infinitely long thin straight wires AB and CD with charge densities $-\frac{12 \mu\text{C}}{\text{m}}$ and $+\frac{12 \mu\text{C}}{\text{m}}$ are lying parallel to y-axis at points $(-1\text{ m}, 0, 0)$ and $(1\text{ m}, 0, 0)$ respectively, as shown in the figure. Find the net electric fiel...
(a) An ac generator consists of a coil of $500$ turns and size $25 ext{ cm} imes 100 ext{ cm}$. It is rotated at an angular speed of $60 ext{ rad/s}$ in a uniform magnetic field $B = 0.4 ext{ T}$ between two fixed pole pieces. If the resistance of the circuit, including that of the coil, is $250 ex...
A charged particle enters with a velocity $\text{v} = (6 \times 10^6\text{ m/s})\hat{\text{i}}$ in a region of magnetic field $\vec{\text{B}} = (0\cdot5\text{ G})\hat{\text{j}}$ and an electric field $\vec{\text{E}}$. If the particle goes straight undeviated in the region, then $\vec{\text{E}}$ equa...
A $2\cdot00\text{ m}$ long wire, ABC made of steel ($\rho = 20 \times 10^{-8}\text{ }\Omega\text{ m}$ at $20\text{\textdegree C}$) consists of two parts AB and BC, each of $1\cdot00\text{ m}$. Part AB has a radius of $0\cdot70\text{ mm}$ while BC has a radius of $0\cdot35\text{ mm}$. Find the magnit...
A charged particle enters with a velocity $\vec{v} = (6 \times 10^6 \text{ m/s})\hat{i}$ in a region of magnetic field $\vec{B} = (0.5 \text{ G})\hat{j}$ and an electric field $\vec{E}$. If the particle goes straight undeviated in the region, then $\vec{E}$ equals :
(A) $\left$120 \frac{\text{N}}{\...
OR
An ac generator consists of a coil of $500$ turns and size $25\text{ cm} \times 100\text{ cm}$. It is rotated at an angular speed of $60\text{ rad/s}$ in a uniform magnetic field $B = 0.4\text{ T}$ between two fixed pole pieces. If the resistance of the circuit, including that of the coil, is $25...
The number of free electrons per unit volume $(\text{m}^3)$ in a wire made of copper (resistivity $1\cdot72 \times 10^{-8}\text{ }\Omega\text{ m}$) is $8\cdot5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wi...
Four point charges $+q$, $-q$, $+q$ and $-q$ are to be arranged respectively at the four corners of a square $ ext{ABCD}$ of the sides $l$. Calculate the amount of :
(i) work done to obtain this arrangement.
(ii) extra work done to bring a point charge $q_0$ at the centre of the square when the char...
(a) Two infinitely long thin straight wires $ ext{AB}$ and $ ext{CD}$ with charge densities $-\frac{12\,\mu ext{C}}{ ext{m}}$ and $+\frac{12\,\mu ext{C}}{ ext{m}}$ are lying parallel to $ ext{y-axis}$ at points $(-1 ext{ m, 0, 0})$ and $(1 ext{ m, 0, 0})$ respectively, as shown in the figure. Find t...
A charged particle enters with a velocity $\text{v} = (6 \times 10^6 \text{ m/s}) \hat{\text{i}}$ in a region of magnetic field $\vec{\text{B}} = (0.5 \text{ G}) \hat{\text{j}}$ and an electric field $\vec{\text{E}}$. If the particle goes straight undeviated in the region, then $\vec{\text{E}}$ equa...
OR
(a) An ac generator consists of a coil of $500$ turns and size $25\text{ cm} \times 100\text{ cm}$. It is rotated at an angular speed of $60\text{ rad/s}$ in a uniform magnetic field $B = 0\cdot4\text{ T}$ between two fixed pole pieces. If the resistance of the circuit, including that of the coil...
Assertion (A): For three point charges to be in equilibrium, they must be collinear.
Reason (R): One of the three charges must have different polarity than rest of the two.
The amplitude of the magnetic field of a plane electromagnetic wave propagating along positive X axis in vacuum is $510 \text{ nT}\hat{k}$ and its angular frequency is $60 \times 10^6$ rad/sec. Write the expression for the electric field ($\vec{E}$).
A charge $q$ is placed inside a sphere of radius '$a$' filled with water and another charge $2q$ is placed inside cube of side '$2a$' which is vacuumed inside. Find the ratio of the flux linked with the sphere to that linked with the cube. (Take relative permittivity of water as $80$)
Which of the following statements about electric field $E$ is incorrect ?
(A) The magnitude of the electric field due to a point charge is proportional to $\frac{1}{r^{2}}$, where $r$ is the distance of the point from the charge.
(B) The magnitude of the electric field is zero at all points in a reg...
An electric dipole is held in a uniform electric field $\vec{E}$ such that its axis makes an angle $\theta$ with $\vec{E}$. Show that the dipole does not undergo any translatory motion. Hence, derive an expression for the torque acting on it and specify its direction.
A dipole is aligned parallel to the electric field. Find the work done in rotating it through an angle (I) $180^{\circ}$, and (II) $90^{\circ}$.
The electric field in the region between $P_1$ and $P_2$ is :
(A) $\frac{V}{d}$
(B) $\frac{2V}{d}$
(C) $\frac{V}{2d}$
(D) $\frac{d}{V}$
(b) (i) Show that Gauss's theorem is consistent with Coulomb's law. Using it, derive an expression for the electric field due to a uniformly charged thin spherical shell of radius $r$ at a point at a distance $y$ from the centre of the shell such that (I) $y > r$, and (II) $y < r$.
(ii) A point cha...
An electric dipole of dipole moment $1.0 \times 10^{-12}$ Cm lies along x-axis. An electric field of magnitude $2.0 \times 10^4 \text{ NC}^{-1}$ is switched on at an instant in the region. The unit vector along the electric field is $\frac{\sqrt{3}}{2}\hat{i} + \frac{1}{2}\hat{j}$. The magnitude of ...
When the switch of the circuit is turned on, the filament of the bulb glows instantaneously because :
(A) the electrons coming from the power source move fast through the initially empty filament.
(B) the filament may be old having low resistance.
(C) electric field is established instantaneously ac...
(a) Differentiate between magnetic flux through an area and magnetic field at a point.
(b) A bar magnet is held with its length along the axis of a closed coil. Initially the south pole of the magnet faces the coil. If the magnet is moved towards the coil, explain how a current is induced in the coi...
The electric field in the region between $ ext{P}_1$ and $ ext{P}_2$ is :
(A) $\frac{\text{V}}{\text{d}}$
(B) $\frac{2\text{V}}{\text{d}}$
(C) $\frac{\text{V}}{2\text{d}}$
(D) $\frac{\text{d}}{\text{V}}$
Two point charges $Q$ and $-q$ are held '$r$' distance apart in free space. A uniform electric field $\vec{E}$ is applied in the region perpendicular to the line joining the two charges. Which one of the following angles will the direction of the net force acting on charge $-q$ make with the line jo...
In an electromagnetic wave travelling in free space, the amplitude of magnetic field is $6.0 \times 10^{-4}\text{ T}$. The amplitude of its electric field is :
(A) $2 \times 10^4\text{ Vm}^{-1}$
(B) $1.5 \times 10^{12}\text{ Vm}^{-1}$
(C) $1.8 \times 10^5\text{ Vm}^{-1}$
(D) $0.3 \times 10^4\text{ V...
Two point charges $+q$ and $-q$ are held at $(a, 0)$ and $(-a, 0)$ in x-y plane. Obtain an expression for the net electric field due to the charges at a point $(0, y)$. Hence, find electric field at a far off point ($y \gg a$).
Three point charges of $-2\text{ nC}$, $-1\text{ nC}$, and $+5\text{ nC}$ are kept at the vertices $A$, $B$ and $C$ of an equilateral triangle of side $0\cdot2\text{ m}$. Find the total amount of work done in shifting the charges from $A$ to $A_1$, $B$ to $B_1$ and $C$ to $C_1$. Here $A_1$, $B_1$ an...
Show that Gauss's theorem is consistent with Coulomb's law. Using it, derive an expression for the electric field due to a uniformly charged thin spherical shell of radius $r$ at a point at a distance $y$ from the centre of the shell such that (I) $y > r$, and (II) $y < r$.
(ii) A point charge of $+2\text{ nC}$ is kept at the origin of a three-dimensional coordinate system. Find the type and magnitude of the charge which should be kept at $(0, 0, -6\text{m})$ so that the potential due to the system becomes zero at $(0, 0, 2\text{m})$.
An electron of mass $m$ and charge $-e$ is revolving anticlockwise around the nucleus of an atom.
(a) Obtain the expression for the magnetic dipole moment ($\mu$) of the atom.
(b) If $\vec{L}$ is the angular momentum of electron, show that $\vec{\mu} = -\left(\frac{e}{2m}\right)\vec{L}$.
Two infinitely long straight wires '1' and '2' are placed $d$ distance apart, parallel to each other, as shown in the figure. They are uniformly charged having charge densities $\lambda$ and $-\frac{\lambda}{2}$ respectively. Locate the position of the point from wire '1' at which the net electric f...
(a) Why is the mass of a nucleus always less than the sum of the masses of its constituents, i.e. free neutrons and free protons ?
(b) How is Coulomb repulsion between protons in a nucleus overcome ? Explain.
Four point charges $Q$ each, are held at the four corners of a square of side $l$. The amount of work done in bringing a charge $Q$ from infinity to the centre of the square will be :
(A) $\frac{Q^2}{\pi \varepsilon_0 l}$
(B) $\frac{\sqrt{2} Q^2}{\pi \varepsilon_0 l}$
(C) $\frac{Q^2}{2\pi \varepsilo...
The dimensions of $(\mu\varepsilon)^{-1}$, where $\varepsilon$ is permittivity and $\mu$ is permeability of a medium, are :
(A) $[M^0 L^1 T^{-1}]$
(B) $[M^0 L^2 T^{-2}]$
(C) $[M^1 L^2 T^{-2}]$
(D) $[M^1 L^{-1} T^1]$
(ii) The ends of six wires, each of resistance $R$ ($= 10\text{ }\Omega$) are joined as shown in the figure. The points A and B of the arrangement are connected in a circuit. Find the value of the effective resistance offered by it to the circuit.
OR
(b) (i) Current $I$ ($= 1\text{ A}$) is passing...
(i) Obtain an expression for the electric field $\vec{E}$ due to a dipole of dipole moment $\vec{p}$ at a point on its equatorial plane and specify its direction. Hence, find the value of electric field :
(I) at the centre of the dipole ($r = 0$), and
(II) at a point $r \gg a$,
where $2a$ is the len...
(a) (i) The electric field in a region is given by $\vec{E} = 40x\text{ }\hat{\text{i}}\text{ N/C}$. Find the amount of work done in taking a unit positive charge from a point $(0, 3\text{m})$ to the point $(5\text{m}, 0)$.
(ii) A charge $Q$ is distributed over two concentric hollow spheres of radii...
(b) (i) Obtain an expression for the electric field $\vec{E}$ due to a dipole of dipole moment $\vec{p}$ at a point on its equatorial plane and specify its direction. Hence, find the value of electric field :
(I) at the centre of the dipole ($r = 0$), and
(II) at a point $r \gg a$,
where $2a$ is the...
A particle of mass $m$ and charge $q$ moving with velocity $v\,\hat{i}$ is subjected to a uniform electric field $E\,\hat{j}$. The particle will initially have a tendency to move in a circle of radius :
(A) $\left(\frac{mv}{qE}\right)$ in x-y plane
(B) $\left(\frac{mv^2}{qE^2}\right)$ in x-z plane
...
OR
(b) (i) Obtain an expression for the electric field $\vec{E}$ due to a dipole of dipole moment $\vec{p}$ at a point on its equatorial plane and specify its direction. Hence, find the value of electric field :
(I) at the centre of the dipole ($r = 0$), and
(II) at a point $r \gg a$,
where $2a$ is ...
(ii) An electric field $\vec{E} = (10x + 5)\hat{i} \text{ N/C}$ exists in a region in which a cube of side $L$ is kept as shown in the figure. Here $x$ and $L$ are in metres. Calculate the net flux through the cube.
The electric field ($E$) and electric potential ($V$) at a point inside a charged hollow metallic sphere are respectively :
(A) $E = 0, V = 0$
(B) $E = 0, V = V_0$ (a constant)
(C) $E \neq 0, V \neq 0$
(D) $E = E_0$ (a constant), $V = 0$
Two point charges of $-5\text{ }\mu\text{C}$ and $2\text{ }\mu\text{C}$ are located in free space at $(-4\text{ cm}, 0)$ and $(6\text{ cm}, 0)$ respectively.
(a) Calculate the amount of work done to separate the two charges at infinite distance.
(b) If this system of charges was initially kept in an...
(ii) You are provided with a large number of $1\text{ }\mu\text{F}$ identical capacitors and a power supply of $1200\text{ V}$. The dielectric medium used in each capacitor can withstand up to $200\text{ V}$ only. Find the minimum number of capacitors and their arrangement, required to build a capac...
An electric field $\vec{E}$ given by :\n$\vec{E} = 100 \hat{i} \frac{\text{N}}{\text{C}}$ for $x > 0$\n$= - 100 \hat{i} \frac{\text{N}}{\text{C}}$ for $x < 0$\nexists in a region. A right circular cylinder of length $10\text{ cm}$ and radius $2\text{ cm}$, is placed in the region such that its axis ...
OR
(b) (i) An electric dipole of dipole moment $p$ consists of point charges $q$ and $-q$, separated by $2\text{a}$. Derive an expression for electric potential in terms of its dipole moment at a point at a distance $x$ ($x \gg \text{a}$) from its centre and lying (I) along its axis, and (II) along...
A small metallic sphere S of charge $+q$ is placed exactly at a point midway between two-point charges A ($+Q$) and B ($+Q$) where $Q \gg q$. If the sphere is slightly displaced towards charge A and released, then :
(A) it will move further towards A
(B) it will move towards B
(C) it will oscilla...
Define electric flux. Is it a scalar or a vector quantity ?
A point charge $q$ is kept at a distance of $\frac{d}{2}$ directly above the centre of a square of side $d$. Use Gauss' law to obtain the expression for the electric flux through the square.
If the point charge is now moved to a point at ...
(i) A parallel plate capacitor $A$ of capacitance $C$ is charged by a battery to a potential $V$. The battery is disconnected and an uncharged identical capacitor $B$ is connected across it. Calculate for the capacitor $A$ the new value of the :
(I) charge
(II) potential difference
(III) energy stor...
A point charge of $10\text{ nC}$ is fixed at the origin of x-y plane. A second point charge of $-20\text{ nC}$ is moved from point $(5\text{ cm}, 0)$ to point $(0, 5\text{ cm})$. The change in the potential energy of the system of the two charges is :
(A) $36\text{ }\mu\text{J}$
(B) $-36\text{ }\mu\...
The electric field due to an infinitely long, straight, uniformly and positively charged wire at a point at distance $r$ from the wire is :
(A) proportional to $\frac{1}{r}$ and is directed outward
(B) proportional to $\frac{1}{r^2}$ and is directed outward
(C) proportional to $\frac{1}{r}$ and is d...
Write Coulomb's law in vector form. Two point charges $q_1 = 10\text{ }\mu\text{C}$ and $q_2 = 20\text{ }\mu\text{C}$ are located at points $(0, 0)$ and $(3\text{ cm}, 4\text{ cm})$ in x-y plane respectively. Find (i) the magnitude of the force exerted on $q_2$ by $q_1$, and (ii) the angle that the ...
33. (a) (i) A parallel plate capacitor A of capacitance C is charged by a battery to a potential $V$. The battery is disconnected and an uncharged identical capacitor B is connected across it. Calculate for the capacitor A the new value of the :
(I) charge
(II) potential difference
(III) energy stor...
A point charge of $20\text{ nC}$ is fixed at the origin of x-y plane. The work done in taking a second point charge of $-50\text{ nC}$ from point $(4\text{ cm}, 0)$ to point $(0, 5\text{ cm})$ is :
(A) $45\text{ }\mu\text{J}$
(B) $-45\text{ }\mu\text{J}$
(C) $90\text{ }\mu\text{J}$
(D) $-90\text{ }\...
The electric field due to a uniformly and negatively charged thin spherical shell at a point outside the shell at a distance $r$ from its centre is :
(A) proportional to $\frac{1}{r}$ and is directed outward
(B) proportional to $\frac{1}{r}$ and is directed inward
(C) proportional to $\frac{1}{r^2}$...
Define electric field. Write its SI unit. A point charge $q = 25\text{ }\mu\text{C}$ is located at the point $(0, 0)$ in x-y plane. Find (i) the magnitude of electric field at point $(3\text{ cm }\text{, } 4\text{ cm})$, and (ii) the angle the field makes with the x-axis.
Define electric flux. Is it a scalar or a vector quantity ?\nA point charge q is kept at a distance of $\frac{\text{d}}{2}$ directly above the centre of a square of side d. Use Gauss' law to obtain the expression for the electric flux through the square.\nIf the point charge is now moved to a point ...
(a) (i) A parallel plate capacitor $A$ of capacitance $C$ is charged by a battery to a potential '$V$'. The battery is disconnected and an uncharged identical capacitor $B$ is connected across it. Calculate for the capacitor $A$ the new value of the :
(I) charge
(II) potential difference
(III) energ...
A cube of side $0\cdot1 \text{ m}$ is placed, as shown in the figure, in a region where electric field $\vec{E} = 500 \text{ x } \hat{i}$ exists. Here $x$ is in meters and $E$ in $\text{NC}^{-1}$. Calculate :
(a) the flux passing through the cube, and
(b) the charge within the cube.
Figure shows variation of Coulomb force (F) acting between two point charges with $\frac{1}{r^2}$, r being the separation between the two charges $(q_1, q_2)$ and $(q_2, q_3)$. If $q_2$ is positive and least in magnitude, then the magnitudes of $q_1, q_2$ and $q_3$ are such that
(A) $q_2 < q_3 < q_1...
A particle of charge q is moving with a velocity $\vec{v}$ at a distance 'd' from a long straight wire carrying a current 'I' as shown in figure. At this instant, it is subjected to a uniform electric field $\vec{E}$ such that the particle keeps moving undeviated. In terms of unit vectors $\hat{i}$,...
Two charges -q each are placed at the vertices A and B of an equilateral triangle ABC. If M is the mid-point of AB, the net electric field at C will point along (A) CA (B) CB (C) MC (D) CM
In the above figure $P, Q$ are the two parallel plates of a capacitor. Plate $Q$ is at positive potential with respect to plate $P$. $ ext{MN}$ is an imaginary line drawn perpendicular to the plates. Which of the graphs shows correctly the variations of the magnitude of electric field strength $E$ a...
Two identical point charges are placed at the two vertices A and B of an equilateral triangle of side $l$. The magnitude of the electric field at the third vertex P is $E$. If a hollow conducting sphere of radius $(l/4)$ is placed at P, the magnitude of the electric field at point P now becomes
(A) ...
(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...
Consider two identical dipoles $D_1$ and $D_2$. Charges $-q$ and $q$ of dipole $D_1$ are located at $(0, 0)$ and $(a, 0)$ and that of dipole $D_2$ at $(0, a)$ and $(0, 2a)$ in $x$-$y$ plane, respectively. The net dipole moment of the system is
(A) $qa$\hat{i} + \hat{j}$$
(B) $-qa$\hat{i} + \hat{j}$$...
In the above figure P, Q are the two parallel plates of a capacitor. Plate Q is at positive potential with respect to plate P. MN is an imaginary line drawn perpendicular to the plates. Which of the graphs shows correctly the variations of the magnitude of electric field strength E along the line MN...
(A) Two points charges $q_1$ and $q_2$ in air are located at $\vec{r}_1$ and $\vec{r}_2$ respectively in a region of uniform external field $\vec{E}$. Obtain an expression for the electrostatic potential energy of the system.
(B) The coulomb force between two point charges is $1.5 \times 10^{-4} \te...
A charged sphere of radius r has surface charge density $\sigma$. The electric field on its surface is E. If the radius of the sphere is doubled, keeping charge density the same, the ratio of the electric field on the old sphere to that on the new sphere will be : (A) 1 (B) $\frac{1}{2}$ (C) $\frac{...
Three point charges $Q_1$, $Q_2$ and $Q_3$ are located in $x - y$ plane at points $(-d, 0)$, $(0, 0)$ and $(d, 0)$ respectively. $Q_1$ and $Q_3$ are identical and $Q_2$ is positive. What will be the nature and value of $Q_1$ so that the potential energy of the system is zero?
OR
(b) (i) An electric dipole (dipole moment $\vec{p} = p\hat{i}$), consisting of charges $-q$ and $q$ separated by distance $2a$, is placed along the x-axis, with its centre at the origin. Show that the potential V, due to this dipole, at a point x, $(x >> a)$ is equal to $\frac{1}{4\pi\varepsilon_...
In a uniform straight wire, conduction electrons move along $+x$ direction. Let $\vec{E}$ and $\vec{j}$ be the electric field and current density in the wire, respectively. Then : (A) $\vec{E}$ and $\vec{j}$ both are along $+x$ direction. (B) $\vec{E}$ and $\vec{j}$ both are along $-x$ direction. (C...
A uniform electric field pointing in positive X-direction exists in a region. Let A be the origin, B be the point on the X-axis at $x = +1 \text{ cm}$ and C be the point on the Y-axis at $y = +1 \text{ cm}$. Then the potential at points A, B and C satisfy. (A) $V_A < V_B$ (B) $V_A > V_B$ (C) $V_A < ...
A cylindrical conductor of length $l$ and cross-section area $A$ is connected to a DC source. Under the influence of electric field set up due to source, the free electrons begin to drift in the opposite direction of the electric field. (I) Draw the curve showing the dependency of drift velocity on ...
(I) State Gauss's theorem in electrostatics. Using this theorem, derive an expression for the electric field due to an infinitely long straight wire of linear charge density $\lambda$. OR (II) (a) Define electric flux and write its SI unit. (b) Use Gauss's law to obtain the expression for the electr...
Two charged particles P and Q, having the same charge but different masses $m_P$ and $m_Q$, start from rest and travel equal distances in a uniform electric field $\vec{E}$ in time $t_P$ and $t_Q$ respectively. Neglecting the effect of gravity, the ratio $\left$ \frac{t_P}{t_Q} \right$$ is :
(A) $\...
Coulomb force $F$ versus $\left(\frac{1}{r^2}\right)$ graphs for two pairs of point charges $(q_1 \text{ and } q_2)$ and $(q_2 \text{ and } q_3)$ are shown in the figure. The ratio of charges $\left(\frac{q_1}{q_3}\right)$ is :
(A) $\sqrt{3}$
(B) $\frac{1}{\sqrt{3}}$
(C) $3$
(D) $\frac{1}{3}$
An electric field E is maintained in a wire of length 'l' and area of cross-section 'a'. Derive the relation between the current density 'j' in the wire and the electric field E.
(b) (i) State Gauss's Law in electrostatics. Apply this to obtain the electric field $\vec{E}$ at a point near a uniformly charged infinite plane sheet.
(ii) Two long straight wires 1 and 2 are kept as shown in the figure. The linear charge density of the two wires are $\lambda_1 = 10 \text{ } \mu\t...
A coil of area of cross-section 'A' has N number of turns. It is rotating with an angular speed $\omega$ inside a uniform magnetic field B. If the total resistance of circuit of coil is R, find :
(a) the maximum current in the circuit.
(b) the flux through the coil when the current is zero.
(c) the ...
The electric potential at a point in an electric field is the work done in bringing a unit positive charge from infinity to this point. If the potential difference between any two points at a surface is zero, the surface is called an equipotential surface. The shape of an equipotential surface can g...
The equipotential surfaces in a uniform electric field acting along $+Z$ direction are :
(A) planes parallel to the XY plane
(B) concentric spherical surfaces
(C) planes parallel to the YZ plane
(D) planes parallel to the XZ plane
The angle between the electric field at a point and outward normal at that point on an equipotential surface is :
(A) $90^{\circ}$
(B) $45^{\circ}$
(C) $30^{\circ}$
(D) $0^{\circ}$
(i) Define electric field. Write its SI units. Derive an expression for electric field due to a point charge at a point. Why must the test charge be as small as possible ?
(ii) An electron and an $\alpha$-particle, both are kept in the same electric field $\vec{E} = E_1 \hat{i} + E_2 \hat{j}$. Find ...
(a) A cell is connected across an external resistance $12\text{ }\Omega$ and supplies $0.25\text{ A}$ current. When the external resistance is increased by $4\text{ }\Omega$, the current reduces to $0.2\text{ A}$. Calculate (i) the emf, and (ii) the internal resistance, of the cell.
OR
(b) Two poi...
Two point charges of $10\text{ }\mu\text{C}$ and $20\text{ }\mu\text{C}$ are located at points $(-4\text{ cm}, 0, 0)$ and $(5\text{ cm}, 0, 0)$ respectively, in a region with electric field $E = \frac{A}{r^2}$, where $A = 2 \times 10^6\text{ N C}^{-1}\text{ m}^2$ and $\vec{r}$ is the position vector...
$E_1$ and $E_2$ are magnitudes of electric field due to a dipole, consisting of charges $-q$ and $+q$ separated by distance $2a$, at points $r$ ($r >> a$) (1) on its axis, and (2) on equatorial plane, respectively. Then $\left(\frac{E_1}{E_2}\right)$ is :
(A) $\frac{1}{4}$
(B) $\frac{1}{2}$
(C) 2...
An electric dipole of dipole moment $5.0 \times 10^{-8}\ \text{Cm}$ is placed in a region where an electric field of magnitude $1.0 \times 10^{3}\ \text{N/C}$ acts at a given instant. At that instant the electric field $\vec{E}$ is inclined at an angle of $30^{\circ}$ to dipole moment $\vec{P}$. The...
OR
A square loop of side $5.0\ \text{cm}$ carries a current of $2.0\ \text{A}$. The magnitude of magnetic dipole moment associated with the loop is :
(A) $1.0 \times 10^{-3}\ \text{Am}^2$
(B) $5.0 \times 10^{-3}\ \text{Am}^2$
(C) $1.0 \times 10^{-2}\ \text{Am}^2$
(D) $5.0 \times 10^{-2}\ \text{...
OR
(b) Two point charges of $3 \mu \text{C}$ and $4 \mu \text{C}$ are kept in air at $(0.3 \text{ m}, 0)$ and $(0, 0.3 \text{ m})$ in x-y plane. Find the magnitude and direction of the net electric field produced at the origin $(0, 0)$.
Two point charges of $10$ $\mu\text{C}$ and $20$ $\mu\text{C}$ are located at points $(-4$ $\text{cm}$, $0$, $0)$ and $(5$ $\text{cm}$, $0$, $0)$ respectively, in a region with electric field $E = \frac{A}{r^2}$, where $A = 2 \times 10^6$ $\text{NC}^{-1} \text{m}^2$ and $\vec{r}$ is the position vec...
OR
A square loop of side $5.0 \text{ cm}$ carries a current of $2.0 \text{ A}$. The magnitude of magnetic dipole moment associated with the loop is :
(A) $1.0 \times 10^{-3} \text{ Am}^2$
(B) $5.0 \times 10^{-3} \text{ Am}^2$
(C) $1.0 \times 10^{-2} \text{ Am}^2$
(D) $5.0 \times 10^{-2} \text{ Am}^2...
OR (b) Two point charges of $3 \,\mu\text{C}$ and $4 \,\mu\text{C}$ are kept in air at $(0.3 \text{ m}, 0)$ and $(0, 0.3 \text{ m})$ in x-y plane. Find the magnitude and direction of the net electric field produced at the origin $(0, 0)$.
OR (b) Two large plane sheets $P_1$ and $P_2$ having charge densities $+\sigma$ and $-3\sigma$ respectively are arranged parallel to each other as shown in the figure. Find the net electric field $(\vec{E})$ at points A, B and C.
Two point charges of $10 \text{ μC}$ and $20 \text{ μC}$ are located at points $(-4 \text{ cm}, 0, 0)$ and $(5 \text{ cm}, 0, 0)$ respectively, in a region with electric field $E = \frac{A}{r^2}$, where $A = 2 \times 10^6 \text{ NC}^{-1} \text{ m}^2$ and $\vec{r}$ is the position vector of the point...
A square loop of side $5.0 \text{ cm}$ carries a current of $2.0 \text{ A}$. The magnitude of magnetic dipole moment associated with the loop is :
A proton is taken from point $P_1$ to point $P_2$, both located in an electric field. The potentials at points $P_1$ and $P_2$ are $-5 \text{ V}$ and $+5 \text{ V}$ respectively. Assuming that kinetic energies of the proton at points $P_1$ and $P_2$ are zero, the work done on the proton is : (A) $-1...
(i) A charge $+ Q$ is placed on a thin conducting spherical shell of radius R. Use Gauss's theorem to derive an expression for the electric field at a point lying (i) inside and (ii) outside the shell. (ii) Show that the electric field for same charge density ($\sigma$) is twice in case of a conduct...
An isolated conductor, with a cavity, has a net charge +Q. A point charge +q is inside the cavity. The charges on the cavity wall and the outer surface are respectively :
(A) 0 and Q
(B) -q and Q - q
(C) -q and Q + q
(D) 0 and Q - q
A proton is taken from point $P_1$ to point $P_2$, both located in an electric field. The potentials at points $P_1$ and $P_2$ are -5 V and +5 V respectively. Assuming that kinetic energies of the proton at points $P_1$ and $P_2$ are zero, the work done on the proton is :
(A) -1.6 $\times 10^{-18}$ ...
(b) (i) A charge + Q is placed on a thin conducting spherical shell of radius R. Use Gauss's theorem to derive an expression for the electric field at a point lying (i) inside and (ii) outside the shell. (ii) Show that the electric field for same charge density ($\sigma$) is twice in case of a condu...
A proton is taken from point $P_1$ to point $P_2$, both located in an electric field. The potentials at points $P_1$ and $P_2$ are $-5\;\text{V}$ and $+5\;\text{V}$ respectively. Assuming that kinetic energies of the proton at points $P_1$ and $P_2$ are zero, the work done on the proton is :
(A) $-1...
A plane electromagnetic wave is travelling in air in + x direction. At a particular moment, its electric field $\vec{E}$ is along + y direction. At that moment, the magnetic field $\vec{B}$ is along :
(A) + z direction and in phase with $\vec{E}$
(B) - z direction and in phase with $\vec{E}$
(C) + ...
A current of $1.6\text{ A}$ flows through a wire when a potential difference of $1.0\text{ V}$ is applied across it. The length and cross-sectional area of the wire are $1.0\text{ m}$ and $1.0 \times 10^{-7}\text{ m}^{2}$ respectively. Calculate :
(a) Electric field across the wire
(b) Current densi...
An electron (charge $-e$, mass $\text{m}$) is revolving around a nucleus, in a hydrogen atom, in a circle of radius $\text{r}$. Derive an expression, in vector form, for the magnetic dipole moment, $\vec{\mu}_{e}$ in terms of its orbital angular momentum $\vec{L}$. What is gyromagnetic ratio ?
(iv) (a) Let $E_1, E_2, E_3$ and $E_4$ be the magnitudes of the electric field between the pairs of plates, I, II, III and IV respectively. Then:
(A) $E_1 > E_2 > E_3 > E_4$
(B) $E_3 > E_4 > E_1 > E_2$
(C) $E_4 > E_3 > E_2 > E_1$
(D) $E_2 > E_3 > E_4 > E_1$
OR (b) (i) A charge + Q is placed on a thin conducting spherical shell of radius R. Use Gauss's theorem to derive an expression for the electric field at a point lying (i) inside and (ii) outside the shell. (ii) Show that the electric field for same charge density ($\sigma$) is twice in case of a co...
The electric field in a region is given by $\vec{E} = (10x + 4)\hat{i}$ where $x$ is in m and E is in N/C. Calculate the amount of work done in taking a unit charge from (i) (5 m, 0) to (10 m, 0) (ii) (5 m, 0) to (5 m, 10 m)
Three point charges, each of charge q are placed on vertices of a triangle ABC, with AB = AC = 5L, BC = 6L. The electrostatic potential at midpoint of side BC will be (A) $\frac{11}{48} \frac{q}{\pi \varepsilon_0 L}$ (B) $\frac{8q}{36\pi \varepsilon_0 L}$ (C) $\frac{5q}{24\pi \varepsilon_0 L}$ (D) $...
The Coulomb force (F) versus $(1/r^2)$ graphs for two pairs of point charges ($q_1$ and $q_2$) and ($q_2$ and $q_3$) are shown in figure. The charge $q_2$ is positive and has least magnitude. Then (A) $q_1 > q_2 > q_3$ (B) $q_1 > q_3 > q_2$ (C) $q_3 > q_2 > q_1$ (D) $q_3 > q_1 > q_2$
A thin spherical conducting shell of radius R has a charge q. A point charge Q is placed at the centre of the shell. Find (i) The charge density on the outer surface of the shell and (ii) the potential at a distance of (R/2) from the centre of the shell.
(b) (i) Using Gauss's law, show that the electric field $\vec{\text{E}}$ at a point due to a uniformly charged infinite plane sheet is given by $\vec{\text{E}} = \frac{\sigma}{2\varepsilon_0} \hat{\text{n}}$ where symbols have their usual meanings. (ii) Electric field $\vec{\text{E}}$ in a region is...
An electric dipole of dipole moment $\vec{p}$ is kept in a uniform electric field $\vec{E}$. The amount of work done to rotate it from the position of stable equilibrium to that of unstable equilibrium will be
(A) $2 \text{pE}$
(B) $-2 \text{pE}$
(C) $\text{pE}$
(D) zero
An infinite long straight wire having a charge density $\lambda$ is kept along y'y axis in x-y plane. The Coulomb force on a point charge q at a point P $(x, 0)$ will be
(A) attractive and $\frac{q\lambda}{2\pi\varepsilon_0 x}$
(B) repulsive and $\frac{q\lambda}{2\pi\varepsilon_0 x}$
(C) attractive ...
(a) Four point charges of $1 \text{ \mu C}$, $-2 \text{ \mu C}$, $1 \text{ \mu C}$ and $-2 \text{ \mu C}$ are placed at the corners A, B, C and D respectively, of a square of side $30 \text{ cm}$. Find the net force acting on a charge of $4 \text{ \mu C}$ placed at the centre of the square.
(a) Define the term 'electric flux' and write its dimensions. (b) A plane surface, in shape of a square of side 1 cm is placed in an electric field $\vec{E} = \left$100 \frac{\text{N}}{\text{C}}\right$\hat{i}$ such that the unit vector normal to the surface is given by $\hat{n} = 0.8\hat{i} + 0.6\ha...
(a) Four point charges of $1 \text{ } \mu\text{C}$, $-2 \text{ } \mu\text{C}$, $1 \text{ } \mu\text{C}$ and $-2 \text{ } \mu\text{C}$ are placed at the corners A, B, C and D respectively, of a square of side $30 \text{ cm}$. Find the net force acting on a charge of $4 \text{ } \mu\text{C}$ placed at...
OR (b) (i) A thin spherical shell of radius R has a uniform surface charge density $\sigma$. Using Gauss' law, deduce an expression for electric field (i) outside and (ii) inside the shell. (ii) Two long straight thin wires AB and CD have linear charge densities $10$ $\mu$C/m and $-20$ $\mu$C/m, res...
(a) Four point charges of $1\,\mu\text{C}$, $-2\,\mu\text{C}$, $1\,\mu\text{C}$ and $-2\,\mu\text{C}$ are placed at the corners A, B, C and D respectively, of a square of side $30\text{ cm}$. Find the net force acting on a charge of $4\,\mu\text{C}$ placed at the centre of the square.
(b) Three point charges, $1\text{ pC}$ each, are kept at the vertices of an equilateral triangle of side $10\text{ cm}$. Find the net electric field at the centroid of triangle.
A circular loop of radius 'a' carries a current 3I through it. Another concentric circular loop of radius 2a carrying a current I is placed perpendicular to the first loop. The dipole moment of the equivalent magnetic dipole for the system is :
(A) $\pi Ia^2$
(B) 5Ia
(C) $5\pi Ia^2$
(D) $7\pi Ia^2$
(i) An electric dipole is kept in a uniform electric field such that the dipole moment is not along the electric field. It will experience :
(A) A net force and a torque
(B) A net force but no torque
(C) A torque but no net force
(D) neither a net force nor a torque
(ii) An electric dipole consists of charges $+q$ and $-q$, separated by distance $2a$. The force acting on a point charge placed at a distance $x$ ($>> a$) on the axis of the dipole is $F$. If the distance of the charge is doubled, the force will become :
(A) $\frac{F}{16}$
(B) $\frac{F}{8}$
(C) $\f...
Two identical small electric dipoles, each of dipole moment $\vec{p}$ are arranged perpendicular to each other such that their negative charges coincide. The magnitude of the net dipole moment of the arrangement will be :
(A) p
(B) 2p
(C) p$\sqrt{2}$
(D) $\frac{p}{\sqrt{2}}$
A molecule with dipole moment $3\cdot0 \times 10^{-30}$ C-m is placed in a uniform electric field of $2 \times 10^4 \text{ NC}^{-1}$. The maximum torque experienced by the molecule is :
(A) $1\cdot5 \times 10^{-34}$ N-m
(B) $6\cdot0 \times 10^{-26}$ N-m
(C) $4\cdot5 \times 10^{34}$ N-m
(D) $6\cdot0 ...
A electric dipole consists of two point charges $+ 2$ pC and $- 2$ pC, separated by a distance $1$ mm. It is kept in a uniform electric field of $2 \times 10^5 \text{ NC}^{-1}$. The amount of work done in rotating it from its position of stable to unstable equilibrium will be :
(A) $2 \times 10^{-10...
OR (b) (i) Obtain an expression for electric potential at a distance r from a point charge Q. (ii) Two point charges of 10 $\mu$C and $-$ 5 $\mu$C are placed at ($-$3 cm, 0) and (6 cm, 0) in an external electric field E = $\frac{A}{r^2}$, where A = 1.8 $\times 10^5$ N C$^{-1}$ m$^2$. Calculate the e...
The diagram below shows the electric field (E) and magnetic field (B) components of an electromagnetic wave at a certain time and location.
In a coil of resistance $100 \, \Omega$ a current is induced by changing the magnetic flux through it. The variation of current with time is as shown in the figure. The magnitude of change in flux through coil is (a) $200 \, \text{Wb}$ (b) $275 \, \text{Wb}$ (c) $225 \, \text{Wb}$ (d) $250 \, \text{...
In a plane electromagnetic wave, the magnetic field oscillates sinusoidally with a frequency of $3 \times 10^{10} \text{ Hz}$, and amplitude $2.4 \times 10^{-8} \text{ T}$. The amplitude of the oscillating electric field is : (a) $1.6 \text{ Vm}^{-1}$ (b) $3.2 \text{ Vm}^{-1}$ (c) $7.2 \text{ Vm}^{-...
(a) (i) What is an electric dipole ? Derive an expression for the torque acting on an electric dipole in a uniform electric field.
(ii) An electric dipole with dipole moment $6 \times 10^{-9}$ $\text{C-m}$ is aligned at an angle of $30^{\circ}$ with the direction of a uniform electric field of magni...
After centuries of efforts, careful studies, experiments and analysis by different scientists, it was concluded that there are two kinds of entities called the electric charge. The property which differentiates the two kinds is called the polarity of charge. The two kinds of charges were named as po...
The inward and the outward electric flux through a Gaussian surface are $2\phi$ and $\phi$ respectively.
(a) What is the net charge enclosed by the surface ?
(b) If the net outward flux through the surface were zero, can it be concluded that there were no charges inside the surface ? Justify your an...
(a) A uniform electric field $E$ of $500 \text{ N/C}$ is directed along $+x$ axis. $\text{O}$, $\text{B}$ and $\text{A}$ are three points in the field having $x$ and $y$ coordinates (in $\text{cm}$) $(0, 0)$, $(4, 0)$ and $(0, 3)$ respectively. Calculate the potential difference between the points (...
A sphere $S_1$ of radius $r_1$ enclosing a charge $Q_1$ is surrounded by another concentric sphere $S_2$ of radius $r_2$ ($r_2 > r_1$). If there is a charge $-Q_2$ in the space between $S_1$ and $S_2$, find the ratio of electric flux through $S_1$ and $S_2$.
(a) A uniform electric field E of $500 \; \text{N/C}$ is directed along +x axis. O, B and A are three points in the field having x and y coordinates (in cm ) (0, 0), (4, 0) and (0, 3) respectively. Calculate the potential difference between the points (i) O and A, and (ii) O and B.
Three point charges $1 \mu\text{C}$, $-1 \mu\text{C}$ and $2 \mu\text{C}$ are kept at the vertices A, B and C respectively of an equilateral triangle of side $1 \text{ m}$. $\text{A}_1$, $\text{B}_1$ and $\text{C}_1$ are the midpoints of the sides AB, BC and CA respectively. Calculate the net amount...
An electric dipole with dipole moment $\vec{P} = P_0 \hat{i} - P_0 \hat{j}$ is placed in an electric field $\vec{E} = E_1 \hat{i} + E_2 \hat{j}$, where $P_0$, $E_1$ and $E_2$ are constants. The torque $\vec{\tau}$ acting on the dipole is :
(a) $P_0 (E_2 - E_1) \hat{k}$
(b) $P_0 (E_2 + E_1) \hat{k}$
...
A uniform electric field is represented as $\vec{E} = \left$3 \times 10^3 \frac{\text{N}}{\text{C}}\right$ \hat{i}$. Find the electric flux of this field through a square of side $10 \text{ cm}$ when the :
(a) plane of the square is parallel to y-z plane, and
(b) the normal to plane of the square ma...
(a) A uniform electric field E of $500 \text{ N/C}$ is directed along +x axis. O, B and A are three points in the field having x and y coordinates (in \text{cm}) $(0, 0)$, $(4, 0)$ and $(0, 3)$ respectively. Calculate the potential difference between the points (i) O and A, and (ii) O and B.
OR
(b) ...
The electric flux through a Gaussian spherical surface enclosing a point charge $q$ is $\phi$. If the charge is replaced by an electric dipole, magnitude of its dipole moment being $2qa$, the flux through the surface will be :
(a) $2\phi$
(b) $\phi$
(c) $\frac{\phi}{2}$
(d) Zero
(b) An electron (charge -e, mass m) is revolving around a positively charged (charge +e) nucleus in a circular orbit of radius r. (i) For a stable orbit, equating the electrostatic Coulomb force between the electron and the nucleus with the requisite centripetal force, obtain an expression for radiu...
(a) (i) Why do we use a small test charge to measure an electric field? (ii) A small stationary positively charged particle is free to move in an electric field. In which direction will it begin to move? (iii) Two point charges Q_1 (40 $\mu$C) and Q_2 (-16 $\mu$C) are placed along x-axis at 0 cm and...
Case Study : A charged body inside an electric field.
A charged latex sphere of mass $1\cdot85 \times 10^{-13} \text{ kg}$ is held stationary in between two horizontal plates which are separated by a distance $0\cdot62 \text{ cm}$. The potential difference between the plates is $1\cdot24 \times 10^3...
Assertion (A) : The electrostatic field $\vec{E}$ is a conservative field.
Reason (R) : Line integral of electric field $\vec{E}$ around a closed path is non zero.
Which of the following statements about nuclear forces is not true? (i) The nuclear force between two nucleons falls rapidly to zero as their distance is more than a few femtometres. (ii) The nuclear force is much weaker than the Coulomb force. (iii) The force is attractive for distances larger than...
The electric potential $V$ as a function of distance $X$ is shown in the figure. The graph of the magnitude of electric field intensity $E$ as a function of $X$ is (i) ..., (ii) ..., (iii) ..., (iv) ...
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17.7 \times 10^{-22}\text{ C/m}^2$. What is electric field intensity $\mathbf{E}$:
(a) in the outer region of the first plate, and
(...
OR
(a) Three charges $-q$, $Q$ and $-q$ are placed at equal distances on a straight line. If the potential energy of the system of these charges is zero, then what is the ratio $Q:q$?
(b)(i) Obtain the expression for the electric field intensity due to a uniformly charged spherical shell of radius $...