A 4 $\mu$F capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 2 $\mu$F capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

1. 3.10×10^-2J
2. 3.33×10^-3 J
3.1.23×10^-2 J
4.2.67×10^-2 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:
1. \(\dfrac{1}{2}QE\)
2. \(QE\)
3. \(2QE\)
4. \(0\)

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 kV, using a material of dielectric constant 3 and dielectric strength of about 10⁷ 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 pF?
 
1. 19 cm²
2. 17 cm²
3. 15 cm²
4. 23 cm²

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

1. 20 cm
2. 30 cm
3. 25 cm
4. 35 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

Four charges of the same magnitude q are placed at four corners of a square of side a. The value of the electric potential at the centre of the square will be: (Where $\mathrm{k}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}$)

1. $\frac{4\mathrm{kq}}{\mathrm{a}}$

2. $4\sqrt{2}\frac{\mathrm{kq}}{\mathrm{a}}$

3. $\frac{4\mathrm{kq}}{\sqrt{2}\mathrm{a}}$

4. $\frac{\mathrm{kq}}{\mathrm{a}\sqrt{2}}$