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 $6\times10^{-3}~\text{m}^2,$ 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. $\dfrac{4q}{\sqrt3\pi\varepsilon_0b}$

2. $\dfrac{8q}{\sqrt3\pi\varepsilon_0b}$

3. $\dfrac{2q}{\sqrt3\pi\varepsilon_0b}$

4. $0$