Consider two points \(1\) and \(2\) in a region outside a charged sphere. Two points are not very far away from the sphere. If \(E\) and \(V\) represent the electric field vector and the electric potential, which of the following is not possible?

1.	\(\left|\vec{E}_1\right|=\left|\vec{E}_2\right|, V_1=V_2\)
2.	\(\vec{E}_1 \neq \vec{E}_2, V_1 \neq V_2\)
3.	\(\vec{E}_1 \neq \vec{E}_2, V_1=V_2\)
4.	\(\left|\vec{E}_1\right|=\left|\vec{E}_2\right|, V_1 \neq V_2\)

A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on the x-axis at x = +1 cm and C be the point on the y-axis at y = +1 cm. Then the potentials at the points A, B and C satisfy 

(1) V_A < V_B

(2) V_A > V_B

(3) V_A < V_C

(4) V_A > V_C

The electric potential at a point (x, y) in the x – y plane is given by V = –kxy. The field intensity at a distance r from the origin varies as 

(1) r²

(2) r

(3) $\frac{1}{r}$

(4) $\frac{1}{r^2}$

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

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