A pendulum bob carries a positive charge. Another positive charge q is held at the point of support, then the time period of bob is (L: length of the simple pendulum)

1.  Greater than $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$

2.  Less than $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$

3.  Equal to $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$

4.  Equal to $2\mathrm{\pi }\sqrt{\frac{2\mathrm{L}}{\mathrm{g}}}$

24 electric dipoles each of dipole moment 2 $\mu$Cm are packed inside a hollow sphere. The net electric flux through the sphere is

1.  $28<mspace\; width="1em"></mspace>{\mathrm{\mu Cm}}^2$

2.  $28<mspace\; width="1em"></mspace>\frac{{\mathrm{\mu Nm}}^2}{\mathrm{C}}$

3.  Zero

4.  Infinity

Which of the following is not the property of charge?

1.  Like point charges repel each other

2.  For an isolated system, the net charge is conserved

3.  Specific charge is invariant

4.  Charge is quantized

Three charges q, and q and -2q are kept at three corners of an equilateral triangle of side a. The magnitude of the electric dipole moment of the arrangement is

1.  2qa

2.  qa$\sqrt{2}$

3.  qa$\sqrt{3}$

4.  qa

Charge Q is distributed uniformly in a spherical region of radius R. Which if the following roughly represents the variation of the electric field (E) versus distance (r) from the center of the sphere?

1.		2.
3.		4.

The electric field at point A is perpendicular to the direction of the dipole moment $\overrightarrow{P}$ of a short electric dipole. The angle $\theta$ is equal to

1.  $0°$

2.  $90°$

3.  ${\tan }^{-1}2$

4.  ${\tan }^{-1}\left(\sqrt{2}\right)$

Two charges are arranged as shown in the figure. If the electric field at the center of the circle is along the negative y-axis, then $\frac{q_1}{q_2}$ is

1.  $\sqrt{3}$

2.  $\frac{1}{\sqrt{3}}$

3.  $\frac{1}{3}$

4.  $\frac{\sqrt{3}}{2}$

A square of side a is lying in xy-plane such that its two adjacent sides are lying on the x and y axes. If an electric field $\overrightarrow{E} = E_0\hat{k}$ is applied on the square, then the flux passing through the square is

1.  $E_0{a}^3$

2.  $\frac{E_0{a}^3}{2}$

3.  $\frac{E_0{a}^3}{3}$

4.  $E_0{a}^2$

The electric field intensity which would be just sufficient to balance the weight of a particle of charge -10 $\mathrm{\mu C}$ and mass 10 mg, is

(Take \(g=10~\text{m/s}^2\))

1. 10 N/C, in an upward direction

2. ${10}^3$ N/C, in a downward direction

3. 10 N/C, in a downward direction

4. ${10}^4$ N/C, in an upward direction

Two charges are placed at a certain distance apart in the air. If a glass slab is introduced between them, then the force between the two charges will

1.  Become zero

2.  Decrease

3.  Increase

4.  Remain the same