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:
1. \(\frac{4q}{\sqrt3\pi\varepsilon_0b}\)
2. \(\frac{8q}{\sqrt3\pi\varepsilon_0b}\)
3. \(\frac{2q}{\sqrt3\pi\varepsilon_0b}\)
4. \(0\)

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?
1. \(1.5\times 10^{5}\) V
2. \(1.0\times 10^{5}\) V
3. \(2.4\times 10^{5}\) V
4. \(2.0\times 10^{5}\) V

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.)
1. -23.1 eV
2. 27.0 eV
3. -27.2 eV
4. 23.7 eV

Two charged conducting spheres of radii a and b are connected to each other by a wire.  The ratio of electric fields at the surfaces of the two spheres is:
1. \(\frac{a}{b}\)
2. \(1\)
3. \(\frac{2a}{b}\)
4. \(\frac{b}{a}\)

What is the area of the plates of a \(2~\text{F}\) parallel plate capacitor, given that the separation between the plates is \(0.5~\text{cm}\)?
1. \(1100~\text{km}^2\)
2. \(1130~\text{km}^2\)
3. \(1110~\text{km}^2\)
4. \(1105~\text{km}^2\)

The equivalent capacitance of the circuit is:

  
1. \(200\) pF
2. \(\frac{200}{3}\) pF
3. \(200\) \(\mu\)F
4. \(150\) pF$$
 

The plates of a parallel plate capacitor have an area of \(90\) cm² 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?
1. \(1.7\times10^{-6}\) J
2. \(2.12\times10^{-6}\) J
3. \(2.55\times10^{-6}\) J
4. \(1.66\times10^{-6}\) J

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?

1. 3.10×10^-2J
2. 3.33×10^-3 J
3.1.23×10^-2 J
4.2.67×10^-2 J

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:
1. \(\dfrac{1}{2}QE\)
2. \(QE\)
3. \(2QE\)
4. \(0\)

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:
1. \(4.0\times 10^{-9}\) F
2. \(4.5\times 10^{-9}\) F
3. \(5.5\times 10^{-9}\) F
4. \(3.3\times 10^{-9}\) F