A source charge Q is kept at a distance of 3 km from a test charge $q_0$. If Q is displaced slightly, then the change in the electric field detected by $q_0$ will be after

1.  10 s

2.  10 ms

3.  10 $\mu$s

4.  10 ns

Two-point charges -q and +9q are kept at r = 12 cm apart as shown. The electric field is zero at:

1.  6 cm from point A toward B

2.  3 cm from point A opposite to B

3.  9 cm from point B towards A

4.  18 cm from the point B towards A

Two-point charges \(+2~\mu\text{C}\) and \(+6~\mu\text{C}\) repel each other with a force of \(60~\text{N}\). If a charge \(-4~\mu\text{C}\) is added to each of them, the force between them will become:
1. \(60~\text{N}\)
2. \(360~\text{N}\)
3. \(20~\text{N}\)
4. \(40~\text{N}\)

A cone of the radius of base 1 m and height 2 m is placed with its base in the xz plane in a region with the uniform electric field $\overrightarrow{\mathrm{E}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>20<mspace\; width="1em"></mspace>\hat{\mathrm{i}}$ V/m as shown in the figure. The magnitude of electric flux linked with the cone is

1.  Zero

2.  10 Vm

3.  20 Vm

4.  40 $\mathrm{\pi }$ Vm

There are two charges 1 $\mathrm{\mu C}$ and 2 $\mathrm{\mu C}$. The ratio of the magnitude of forces acting on them due to their interaction will be

1.  1 : 2

2.  2 : 1

3.  1 : 1

4.  1 : 4 

The dielectric constant for the metal in electrostatics is

1.  1

2.  0

3.  81

4.  Infinite

A cube of side a has a charge \(q\) at each of its vertices. The net electric field intensity at its centre is: 
(\(r\) is the distance between a corner and the centre, and \(k=1/4\pi \varepsilon_0\) )
1. zero
2. \(kq/r^2\)
3. \(12kq/r^2\)
4. \(6kq/r^2\)

The torque acting on an electric dipole of the dipole moment $\overrightarrow{P}$ in a uniform electric field $\overrightarrow{E}$ is

1.  $\overrightarrow{P}$.$\overrightarrow{E}$

2.  $\overrightarrow{P}$ x $\overrightarrow{E}$

3.  Zero

4.  $\overrightarrow{E}$ x $\overrightarrow{P}$

The unit of electric permittivity is

1.  joule/coulomb

2.  volt/${\mathrm{meter}}^2$

3.  farad/meter

4.  henry/meter

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 $2\mathrm{\pi }\sqrt{\frac{2\mathrm{L}}{\mathrm{g}}}$