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:

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?

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:

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

The equivalent capacitance of the circuit is: