The capacitance of a parallel plate capacitor with air as a medium is \(6~\mu\text{F}.\) With the introduction of a dielectric medium, the capacitance becomes \(30~\mu\text{F}.\)$$ The permittivity of the medium is:
\(\left(\varepsilon_0=8.85 \times 10^{-12} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\right )\)
1. \(1.77 \times 10^{-12}~ \text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
2. \(0.44 \times 10^{-10} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
3. \(5.00 ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
4. \(0.44 \times 10^{-13} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\)

A short electric dipole has a dipole moment of \(16 \times 10^{-9} ~\text{C-}\text{m}.\) The electric potential due to the dipole at a point at a distance of \(0.6~\text{m}\) from the centre of the dipole situated on a line making an angle of \(60^{\circ}\) with the dipole axis is:
\(\left( \dfrac{1}{4\pi \varepsilon_0}= 9\times 10^{9}~\text{N-m}^2/\text{C}^2 \right)\)
1. \(200~\text{V}\)
2. \(400~\text{V}\)
3. zero
4. \(50~\text{V}\)

In a certain region of space with volume \(0.2~\text m^3,\) the electric potential is found to be \(5~\text V\) throughout. The magnitude of the electric field in this region is:
1. \(0.5~\text {N/C}\) 
2. \(1~\text {N/C}\) 
3. \(5~\text {N/C}\) 
4. zero

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 \(8~p\text{F}.\). 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. \(48~p\text{F}\)
2. \(8~p\text{F}\)
3. \(96~p\text{F}\)
4. \(60~p\text{F}\)

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. \(1.5\times10^{-8}~\text J\)