The plates of a parallel plate capacitor have an area of \(90~\text{cm}^2\) each and are separated by \(2.5~\text{mm}.\) The capacitor is charged by connecting it to a \(400~\text{V}\) supply. How much electrostatic energy is stored by the capacitor?
1. \(1.7\times10^{-6}~\text J\) 
2. \(2.12\times10^{-6}~\text J\) 
3. \(2.55\times10^{-6}~\text J\) 
4. \(1.66\times10^{-6}~\text J\) 

A \(4 ~\mu \text{F}\) capacitor is charged by a \(200 ~\text {V}\) supply. It is then disconnected from the supply and is connected to another uncharged \(2 ~\mu \text{F}\) capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?
1. \(3.10 \times 10^{-2} ~\text {J}\)
2. \(3.33 \times 10^{-3} ~\text {J}\)
3. \(1.23 \times 10^{-2} ~\text {J}\)
4. \(2.67 \times 10^{-2} ~\text {J}\)

If \(Q\) is the charge on the capacitor, and \(E\) is the magnitude of the electric field between the plates. Then force on each plate of a parallel plate capacitor has a magnitude equal to:

A spherical capacitor has an inner sphere of radius \(12\) cm and an outer sphere of radius \(13\) cm. The outer sphere is earthed and the inner sphere is given a charge of \(2.5\) $\mu$C. The space between the concentric spheres is filled with a liquid of dielectric constant \(32.\) The capacitance of the capacitor is:
1. \(4.0\times 10^{-9}\) F
2. \(4.5\times 10^{-9}\) F
3. \(5.5\times 10^{-9}\) F
4. \(3.3\times 10^{-9}\) F

A cylindrical capacitor has two co-axial cylinders of length \(15~\text{cm}\) and radii \(1.5~\text{cm}\) and \(1.4~\text{cm}\). The outer cylinder is earthed and the inner cylinder is given a charge of \(3.5~\mu \text{C}\).  The capacitance of the system is:
1. \(3.4 \times10^{-10}~\text{F}\) 
2. \(1.2 \times10^{-10}~\text{F}\)
3. \(4.8 \times10^{-9}~\text{F}\)  
4. \(2.5 \times10^{-9}~\text{F}\)  

A parallel plate capacitor is to be designed with a voltage rating of \(1 ~\text{kV},\) using a material of dielectric constant \(3\) and dielectric strength of about \(10^7 ~\text{V m}^{-1}.\) For safety, we should like the field never to exceed, say \(10\%\) of the dielectric strength. What minimum area of the plates is required to have a capacitance of \(50~\text{pF}?\)
1. \(19~\text{cm}^2\)
2. \(17~\text{cm}^2\)
3. \(15~\text{cm}^2\)
4. \(23~\text{cm}^2\)

In a Van-de-Graff type generator, a spherical metal shell is to be a \(15 \times 10^6 ~\text {V}\) electrode. The dielectric strength of the gas surrounding the electrode is $\mathrm{}$\(5 \times 10^7 ~\text {V/m}.\) What is the minimum radius of the spherical shell required?

1. \(20~\text{cm}\)
2. \(30~\text{cm}\)
3. \(25~\text{cm}\)
4. \(35~\text{cm}\)

Three isolated equal charges are placed at the three corners of an equilateral triangle as shown in the figure. The statement which is true for net electric potential V and net electric field intensity E at the centre of the triangle is:

1. $\mathrm{E}=0, \mathrm{V}=0$

2. $\mathrm{V}=0, \mathrm{E}\ne 0$

3. $\mathrm{V}\ne 0, \mathrm{E}=0$

4. $\mathrm{V}\ne 0, \mathrm{E}\ne 0$

The potential at a point 0.1 m from an isolated point charge is +100 volt. The nature of the point charge is:

1. Positive

2. Negative

3. Zero

4. Either positive or zero

A charge of 10$\mathrm{\mu }$C is placed at the origin of the x-y coordinate system. The potential difference between two points (0, a) and (a, 0) in volt will be:

1. $\frac{9\times {10}^4}{\mathrm{a}}$

2. $\frac{9\times {10}^4}{\mathrm{a}\sqrt{2}}$

3. $\frac{9\times {10}^4}{2\mathrm{a}}$

4. Zero