Electrostatic and Magnetostatic Boundary Problems - Electromagnetic theory - Physics Previous Year Questions

1

2007 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2007

Four point charges are placed in a plane at the following positions: \( +Q \) at (1, 0), \( -Q \) at (-1, 0), \( +Q \) at (0, 1) and \( -Q \) at (0, -1). At large distances the electrostatic potential due to this charge distribution will be dominated by the

A

monopole moment.

B

dipole moment.

C

quadrupole moment.

D

octopole moment.

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2

2007 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2007

Four point charges are placed in a plane at the following positions: +Q at (1, 0), -Q at (-1, 0), +Q at (0, 1) and -Q at (0, -1). At large distances the electrostatic potential due to this charge distribution will be dominated by the

A

monopole moment.

B

dipole moment.

C

quadrupole moment.

D

octopole moment.

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3

2007 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2007

For the circuit shown, the potential difference (in Volts) across R_L is

A

48

B

52

C

56

D

65

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4

2007 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2007

For the circuit shown, the potential difference (in Volts) across \( R_1 \) is

A

48

B

52

C

56

D

65

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5

2007 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2007

The bound surface and volume charge densities are given, respectively, by

A

\(-k|\vec{r}|\) and \(3k\)

B

\(k|\vec{r}|\) and \(-3k\)

C

\(k|\vec{r}|\) and \(-4\pi kR\)

D

\(-k|\vec{r}|\) and \(4\pi kR\)

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6

2007 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2007

The electric field \(\vec{E}\) at a point \(\vec{r}\) outside the sphere is given by

A

\(\vec{E} = 0\)

B

\(\vec{E} = \frac{kR(R^2 - r^2)}{\epsilon_0 r^3} \vec{r}\)

C

\(\vec{E} = \frac{kR(R^2 - r^2)}{\epsilon_0 r^3} \vec{r}\)

D

\(\vec{E} = \frac{3k(r - R)}{4 \pi \epsilon_0 r^3} \vec{r}\)

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7

2008 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2008

A dielectric sphere is placed in a uniform electric field directed along the positive y-axis. Which one of the following represents the correct equipotential surfaces?

A

Image of option (A)

B

Image of option (B)

C

Image of option (C)

D

Image of option (D)

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8

2008 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2008

A circular disc of radius \( a \) on the xy plane has a surface charge density \( \sigma = \frac{\sigma_0 r \cos \theta}{a} \). The electric dipole moment of this charge distribution is

A

\(\frac{\sigma_0 \pi a^3}{4} \hat{x} \)

B

\(\frac{\sigma_0 \pi a^3}{4} \hat{y} \)

C

\(-\frac{\sigma_0 \pi a^3}{4} \hat{x} \)

D

\(-\frac{\sigma_0 \pi a^3}{4} \hat{y} \)

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9

2008 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2008

The electric field in different regions are

A

$\vec{E}=0$ for $rd$

B

$\vec{E}=\frac{-Q}{4\pi\epsilon_0 r^2}\hat{r}$ for $rd$

C

$\vec{E}=\frac{-Q}{4\pi\epsilon_0 r^2}\hat{r}$ for $rd$

D

$\vec{E}=0$ for $rd$

Check answer

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10

2008 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2008

In order to have equal surface charge densities on the outer surfaces of both the shells, the following conditions should be satisfied

A

d = 4b and c = 2a

B

d = 2b and c = √2a

C

d = √2b and c > a

D

d > b and c = √2a

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11

2009 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2009

An electrostatic field \(\vec{E}\) exists in a given region R. Choose the WRONG statement.

A

Circulation of \(\vec{E}\) is zero

B

\(\vec{E}\) can always be expressed as the gradient of a scalar field

C

The potential difference between any two arbitrary points in the region R is zero

D

The work done in a closed path lying entirely in R is zero

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12

2009 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2009

A cylindrical rod of length L and radius r, made of an inhomogeneous dielectric, is placed with its axis along the z direction with one end at the origin as shown below.
If the rod carries a polarization, \(\vec{P} = (5z^2 + 7)\hat{k}\), the volume bound charge inside the dielectric is

A

Zero

B

\(10\pi r^2 L\)

C

\(-5\pi r^2 L\)

D

\(-5\pi r^2 L^2\)

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13

2009 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2009

Assuming an ideal voltage source, Thevenin's resistance and Thevenin's voltage respectively for the above circuit are

A

15\(\Omega\) and 7.5 V

B

20\(\Omega\) and 5 V

C

10\(\Omega\) and 10 V

D

30\(\Omega\) and 15 V

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14

2010 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2010

An insulating sphere of radius a carries a charge density \(\rho(\vec{r}) = \rho_0 (a^2 - r^2) \cos \theta\), \(r < a\). The leading order term for the electric field at a distance d, far away from the charge distribution, is proportional to

A

\(d^{-1}\)

B

\(d^{-2}\)

C

\(d^{-3}\)

D

\(d^{-4}\)

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15

2010 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2010

Two magnetic dipoles of magnitude \( m \) each are placed in a plane as shown.
The energy of interaction is given by

A

Zero

B

\(\frac{\mu_0}{4\pi} \frac{m^2}{d^3} \)

C

\(\frac{3\mu_0}{2\pi} \frac{m^2}{d^3} \)

D

\(-\frac{3\mu_0}{8\pi} \frac{m^2}{d^3} \)

Check answer

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16

2011 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2011

Two charges q and 2q are placed along the x-axis in front of a grounded, infinite conducting plane, as shown in the figure. They are located respectively at a distance of 0.5 m and 1.5 m from the plane. The force acting on the charge q is

A

\(\frac{1}{4\pi\epsilon_0} \frac{7q^2}{2} \)

B

\(\frac{1}{4\pi\epsilon_0} 2q^2 \)

C

\(\frac{1}{4\pi\epsilon_0} q^2 \)

D

\(\frac{1}{4\pi\epsilon_0} \frac{q^2}{2} \)

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17

2011 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2011

Two charges \(q\) and \(2q\) are placed along the \(x\)-axis in front of a grounded, infinite conducting plane, as shown in the figure. They are located respectively at a distance of \(0.5\) m and \(1.5\) m from the plane. The force acting on the charge \(q\) is

A

\(\frac{1}{4\pi\varepsilon_0} \frac{7q^2}{2}\)

B

\(\frac{1}{4\pi\varepsilon_0} 2q^2\)

C

\(\frac{1}{4\pi\varepsilon_0} q^2\)

D

\(\frac{1}{4\pi\varepsilon_0} \frac{q^2}{2}\)

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18

2011 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2011

A magnetic dipole of dipole moment \(\vec{m}\) is placed in a non-uniform magnetic field \(\vec{B}\). If the position vector of the dipole is \(\vec{r}\), the torque acting on the dipole about the origin is

A

\(\vec{r} \times (\vec{m} \times \vec{B})\)

B

\(\vec{r} \times \vec{\nabla} (\vec{m} \cdot \vec{B})\)

C

\(\vec{m} \times \vec{B}\)

D

\(\vec{m} \times \vec{B} + \vec{r} \times \vec{\nabla} (\vec{m} \cdot \vec{B})\)

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19

2011 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2011

A spherical conductor of radius \( a \) is placed in a uniform electric field \( \vec{E} = E_0 \hat{k} \). The potential at a point \( P(r,\theta) \) for \( r > a \), is given by \( \phi(r,\theta) = \text{constant} - E_0 r \cos\theta + \frac{E_0 a^3}{r^2} \cos\theta \) where \( r \) is the distance of P from the centre O of the sphere and \( \theta \) is the angle OP makes with the z-axis. The charge density on the sphere at \( \theta = 30^\circ \) is

A

\(3\sqrt{3}\epsilon_0 E_0 / 2 \)

B

\(3\epsilon_0 E_0 / 2 \)

C

\(\sqrt{3}\epsilon_0 E_0 / 2 \)

D

\(\epsilon_0 E_0 / 2 \)

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20

2011 · Physics · Electromagnetic theory · Electrostatic and Magnetostatic Boundary Problems

Physics (PH) 2011

A spherical conductor of radius \( a \) is placed in a uniform electric field \( \vec{E} = E_0 \hat{k} \). The potential at a point \( P(r, \theta) \) for \( r > a \), is given by \[ \phi(r, \theta) = \text{constant} - E_0 r \cos\theta + \frac{E_0 a^3}{r^2} \cos\theta \] where \( r \) is the distance of P from the centre O of the sphere and \( \theta \) is the angle OP makes with the z-axis. The charge density on the sphere at \( \theta = 30^\circ \) is

A

\(3\sqrt{3}\epsilon_0 E_0 / 2 \)

B

\(3\epsilon_0 E_0 / 2 \)

C

\(\sqrt{3}\epsilon_0 E_0 / 2 \)

D

\(\epsilon_0 E_0 / 2 \)

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