The capacitance of a parallel plate capacitor with air as medium is $6\mathrm{\mu F}$. With the introduction of a dielectric medium, the capacitance becomes 30 $\mathrm{\mu F}$. The permittivity of the medium is: ${\mathrm{\epsilon }}_{\mathrm{o}} = 8.85\times {10}^{-12} {\mathrm{C}}^2 {\mathrm{N}}^{-1} {\mathrm{m}}^{-2}$

A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. The potential at the center of the hexagon is:

$$\begin{gathered} \left(1\right) 2.7\times {10}^6 V \\ \left(2\right) 0 \\ \left(3\right) 3.7\times {10}^6 V \\ \left(4\right) 2.0\times {10}^6 V \end{gathered}$$

A parallel plate capacitor with air between the plates has a capacitance of 8pF. What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?

Three capacitors connected in series have a capacitance of 9pF each. The potential difference across each capacitor if the combination is connected to a 120 V supply is:

The equivalent capacitance of the circuit is:

Four charges of the same magnitude q are placed at four corners of a square of side a. The value of the electric potential at the centre of the square will be: (Where $\mathrm{k}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}$)

Two identical positive charges are placed on the y-axis at y=-a and y=+a. The variation of V (the electric potential) along the x-axis is shown by the graph:

Three capacitors of capacitances 2 pF, 3 pF, and 4 pF are connected in parallel. The charge on 4 pF capacitor if the combination is connected to a 100 V supply is:

$$\begin{gathered} \left(1\right) 4\times {10}^{-10} C \\ \left(2\right) 3\times {10}^{-9} C \\ \left(3\right) 2\times {10}^{-10} C \\ \left(4\right) 1\times {10}^{-9} C \end{gathered}$$

Two charges 5×10^-8 C and -3x10^-8 C are located 16 cm apart from each other. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

In a parallel plate capacitor with air between the plates, each plate has an area of $6\times {10}^{-3} m^2,$ and the distance between the plates is 3 mm. The capacitance of the capacitor is:

A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor?

$$\begin{gathered} \left(1\right) 3.1\times {10}^{-8} J \\ \left(2\right) 2.9\times {10}^{-8} J \\ \left(3\right) 3.3\times {10}^{-8} J \\ \left(4\right) 1.5\times {10}^{-8} J \end{gathered}$$

A 600 pF capacitor is charged by a 200V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?

$$\begin{gathered} \left(1\right) 5\times {10}^{-6} J \\ \left(2\right) 6\times {10}^{-5} J \\ \left(3\right) 6\times {10}^{-6} J \\ \left(4\right) 5\times {10}^{-5} J \end{gathered}$$

A charge of 8 mC is located at the origin. The work done in taking a small charge of $-2\times {10}^{-9} C$  from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm) is:

$$\begin{gathered} \left(1\right) 3.27 J \\ \left(2\right) 1.27 J \\ \left(3\right) 0.27 J \\ \left(4\right) 2.70 J \end{gathered}$$

A cube of side b has a charge q at each of its vertices. The potential due to this charge array at the center of the cube is:

$$\begin{gathered} \left(1\right) \frac{4q}{\sqrt{3}\pi {\epsilon }_{0}b} \\ \left(2\right) \frac{8q}{\sqrt{3}\pi {\epsilon }_{0}b} \\ \left(3\right) \frac{2q}{\sqrt{3}\pi {\epsilon }_{0}b} \\ \left(4\right) 0 \end{gathered}$$

Two tiny spheres carrying charges of 1.5 µC and 2.5 µC are located 30 cm apart. What is the potential at a point 10 cm from the midpoint in a plane normal to the line and passing through the mid-point?

$$\begin{gathered} \left(1\right) 1.5\times {10}^5 V \\ \left(2\right) 1\times {10}^5 V \\ \left(3\right) 2.4\times {10}^5 V \\ \left(4\right) 2\times {10}^5 V \end{gathered}$$

In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å. The potential energy of the system in eV is:
(Taking the zero of the potential energy at an infinite separation of the electron from the proton.)

Which graph best represents the variation of electric potential as a function of distance from the centre of a uniformly charged solid sphere of radius R?

The plates of a parallel plate capacitor have an area of 90 $c{m}^2$ each and are separated by 2.5 mm. The capacitor is charged by connecting it to a 400 V supply. How much electrostatic energy is stored by the capacitor?

$$\begin{gathered} \left(1\right) 1.17\times {10}^{-6} J \\ \left(2\right) 2.12\times {10}^{-6} J \\ \left(3\right) 2.55\times {10}^{-6} J \\ \left(4\right) 1.66\times {10}^{-6} J \end{gathered}$$

A 4 $\mu$F capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 2 $\mu$F capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

$$\begin{gathered} \left(1\right) 3.10\times {10}^{-2} J \\ \left(2\right) 3.33\times {10}^{-3} J \\ \left(3\right) 1.23\times {10}^{-2} J \\ \left(4\right) 2.67\times {10}^{-2} J \end{gathered}$$

If Q is the charge on the capacitor, and E is the magnitude of the electric field between the plates. Then force on each plate of a parallel plate capacitor has a magnitude equal to:

$$\begin{gathered} \left(1\right) \frac{1}{2}QE \\ \left(2\right) QE \\ \left(3\right) 2QE \\ \left(4\right) 0 \end{gathered}$$

A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 $\mu$C. The space between the concentric spheres is filled with a liquid of dielectric constant 32. The capacitance of the capacitor is:

$$\begin{gathered} \left(1\right) 4.0\times {10}^{-9} F \\ \left(2\right) 4.5\times {10}^{-9} F \\ \left(3\right) 5.5\times {10}^{-9} F \\ \left(4\right) 3.3\times {10}^{-9} F \end{gathered}$$

A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge Of 3.5 $\mu$C.  The capacitance of the system is:

$$\begin{gathered} \left(1\right) 3.4\times {10}^{-10} F \\ \left(2\right) 1.2\times {10}^{-10} F \\ \left(3\right) 4.8\times {10}^{-9} F \\ \left(4\right) 2.5\times {10}^{-9} F \end{gathered}$$

A parallel plate capacitor is to be designed with a voltage rating of 1 kV, using a material of dielectric constant 3 and dielectric strength of about 10⁷ V m^-1. For safety, we should like the field never to exceed, say 10% of the dielectric strength. What minimum area of the plates is required to have a capacitance of 50 pF?

$$\begin{gathered} \left(1\right) 19 c{m}^2 \\ \left(2\right) 17 c{m}^2 \\ \left(3\right) 15 c{m}^2 \\ \left(4\right) 23 c{m}^2 \end{gathered}$$

In a Van-de-Graff type generator, a spherical metal shell is to be a 15×${10}^6$ V electrode. The dielectric strength of the gas surrounding the electrode is $5\times {10}^7$ V/m. What is the minimum radius of the spherical shell required?

The potential at a point 0.1 m from an isolated point charge is +100 volt. The nature of the point charge is:

A charge of 10$\mathrm{\mu }$C is placed at the origin of the x-y coordinate system. The potential difference between two points (0, a) and (a, 0) in volt will be:

The electric potential at a distance of 3 m on the axis of a short dipole of dipole moment $4\times {10}^{-12}$ coulomb-metre is:

The electric potential in volts due to an electric dipole moment of $2\times {10}^{-8}$ coulomb-metre at a distance of 3m on a line making an angle of $60°$with the axis of the dipole is:

An electric dipole of length 2 cm is placed with its axis making an angle of $30°$ to a uniform electric field ${10}^5 \mathrm{N}/\mathrm{C}$. If it experiences a torque of $10\sqrt{3} \mathrm{Nm}$, then the potential energy of the dipole:

A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is: