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 center is: 

( r is the distance between a corner and the center and k = 1/4πε₀ )

1.  Zero

2.  $k\frac{q}{r^2}$

3.  $k\frac{12q}{r^2}$

4.  $k\frac{6q}{r}$

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

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