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.

1. 10 cm from the positive charge between the charges.
2. 40 cm from the positive charge between the charges.
3. 10 cm from the negative charge between the charges.
4. 40 cm from the negative charge between the charges.

In a parallel plate capacitor with air between the plates, each plate has an area of $\mathrm{}$\(6\times10^{-3}~\text{m}^2\), and the distance between the plates is \(3~\text{mm}\). The capacitance of the capacitor is:
1. \(16.12~\text{pF}\)
2. \(17.71~\text{pF}\)
3. \(15.01~\text{pF}\)
4. \(11.32~\text{pF}\)

A \(12\) pF capacitor is connected to a \(50\) V battery. How much electrostatic energy is stored in the capacitor?
1. \(3.1\times10^{-8}\) J
2. \(2.9\times10^{-8}\) J
3. \(3.3\times10^{-8}\) J
4. \(1.5\times10^{-8}\) J

A \(600\) pF capacitor is charged by a \(200\) V 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?
1. \( 5 \times 10^{-6} \) J
2. \( 6 \times 10^{-5} \) J
3. \( 6 \times 10^{-6} \) J
4. \( 5 \times 10^{-5}\) J

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:

1. 3.27 J
2. 1.27 J
3. 0.27 J
4. 2.70 J

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. \(1105~\text{km}^2\)