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 \(9~\text{pF}\) each. The potential difference across each capacitor if the combination is connected to a \(120~\text V\) supply is:
1. \(10~\text V\) 
2. \(20~\text V\) 
3. \(30~\text V\) 
4. \(40~\text V\) 

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

Two charges \(5×10^{-8}~\text C\) and \(-3\times 10^{-8}~\text C\) are located \(16~\text{cm}\) 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 $\mathrm{}$\(6\times10^{-3}~\text{m}^2\), 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 \(12~\text{pF}\) capacitor is connected to a \(50~\text V\) battery. How much electrostatic energy is stored in the capacitor?
1. \(3.1\times10^{-8}~\text J\)
2. \(2.9\times10^{-8}~\text J\)
3. \(3.3\times10^{-8}~\text J\)
4. \(1.5\times10^{-8}~\text J\)

A \(600~\text{pF}\) capacitor is charged by a \(200~\text V\) supply. It is then disconnected from the supply and is connected to another uncharged \(600~\text{pF}\) capacitor. How much electrostatic energy is lost in the process?
1. \( 5 \times 10^{-6} ~\text J\) 
2. \( 6 \times 10^{-5} ~\text J\) 
3. \( 6 \times 10^{-6} ~\text J\) 
4. \( 5 \times 10^{-5}~\text J\) 

A charge of \(8~\text{mC}\) is located at the origin. The work done in taking a small charge of  \(-2\times 10^{-9}~\text C\) from a point \(P (0, 0, 3~\text{cm})\) to a point \(Q (0, 4~\text{cm}, 0),\) via a point \(R (0, 6~\text{cm}, 9~\text{cm})\) is:
1. \(3.27~\text J\)
2. \(1.27~\text J\)
3. \(0.27~\text J\)
4. \(2.70~\text J\)

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. \(0\)