Two equal point charges are fixed at x = –a and x = +a on the x-axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q, when it is displaced by a small distance x along the x-axis, is approximately proportional to 

(1) x

(2) x²

(3) x³

(4) 1/x

An elementary particle of mass \(m\) and charge \(+e\) is projected with velocity \(v\) at a much more massive particle of charge \(Ze\), where \(Z>0\). What is the closest possible approach of the incident particle?

A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –3Q, the new potential difference between the same two surfaces is 

(1) V

(2) 2V

(3) 4V

(4) –2V

A piece of cloud is having area \(25\times 10^{6}~\text{m}^2\) and an electric potential of \(10^5\) volts. If the height of cloud is \(0.75~\text{km}\), then find the energy of the electric field between the earth and the cloud will be: 
1. \(250~\text{J}\)
2. \(759~\text{J}\)
3. \(1225~\text{J}\)
4. \(1475~\text{J}\)

A parallel plate air capacitor has a capacitance of 100 μF. The plates are at a distance d apart. If a slab of thickness $t(t\le d)$ and dielectric constant 5 is introduced between the parallel plates, then the capacitance will be 

(1) 50 μμF

(2) 100 μμF

(3) 200 μμF

(4) 500 μμF

Capacitance of a capacitor made by a thin metal foil is 2 μF. If the foil is folded with paper of thickness 0.15 mm, dielectric constant of paper is 2.5 and width of paper is 400 mm, then length of foil will be 

(1) 0.34 m

(2) 1.33 m

(3) 13.4 m

(4) 33.9 m

A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed. If x is the separation between the plates, the time rate of change of electrostatic energy of the capacitor is proportional to:

(1) x^–2

(2) x

(3) x^–1

(4) x²

To form a composite 16 μF, 1000 V capacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors

1. 40

2. 32

3. 8

4. 2

Figure given below shows two identical parallel plate capacitors connected to a battery with switch S closed. The switch is now opened and the free space between the plate of capacitors is filled with a dielectric of dielectric constant 3. What will be the ratio of total electrostatic energy stored in both capacitors before and after the introduction of the dielectric 

(1) 3 : 1

(2) 5 : 1

(3) 3 : 5

(4) 5 : 3

A parallel plate capacitor of capacitance \(C\) is connected to a battery and is charged to a potential difference \(V\). Another capacitor of capacitance \(2C\) is connected to another battery and is charged to potential difference \(2V.\) The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is?
1. zero
2. \(\frac{25 C V^{2}}{6}\)
3. \(\frac{3 C V^{2}}{2}\)
4. \(\frac{9 C V^{2}}{2}\)