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:
1. \(2.7\times10^{6}\)  V
2. 0
3. \(3.7\times10^{6}\) V
4. \(2.0\times10^{6}\) V

A parallel plate capacitor with air between the plates has a capacitance of \(8~\text{pF}\). 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 \(6\)?
1. \(48~\text{pF}\)
2. \(8~\text{pF}\)
3. \(96~\text{pF}\)
4. \(60~\text{pF}\)

Three capacitors connected in series have a capacitance of \(9\) pF each. The potential difference across each capacitor if the combination is connected to a \(120\) V supply is:
1. \(10\) V
2. \(20\) V
3. \(30\) V
4. \(40\) V

Three capacitors of capacitances \(2\) pF, \(3\) pF, and \(4\) pF are connected in parallel. The charge on the \(4\) pF capacitor, if the combination is connected to a \(100\) V supply, is:
1.\(4\times10^{-10}\) C
2. \(3\times10^{-9}\) C
3. \(2\times10^{-10}\) C
4. \(1\times10^{-9}\) C

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. \(0\)