(i) Calculate work done in separating two electrons form a distance of 1 m to 2 m in air, where e is electric charge

Question

Read the following paragraph and answer the questions that follow. 

This energy possessed by a system of charges by virtue of their positions. When two like charges lie infinite distance apart, their potential energy is zero because no work has to be done in moving one charge at infinite distance from the other.

In carrying a charge q from point A to point B, work done W = q(V_A – V_B). This work may appear as change in KE/PE of the charge. The potential energy of two charges q₁ and q₂ at a distance r in air is \(\frac{q_1 q_2}{4\pi \epsilon_0 r}.\) It is measured in joule. It may be positive, negative or zero depending on the signs of q₁ and q₂.

(i) Calculate work done in separating two electrons form a distance of 1 m to 2 m in air, where e is electric charge and k is electrostatic force constant. 

(a) ke² 

(b) e² /2 

(c) –ke² /2 

(d) zero

(ii) Four equal charges q each are placed at four corners of a square of side a each. Work done in carrying a charge –q from its centre to infinity is

(a) zero

(b) \(\frac{\sqrt {2}q^2}{\pi \epsilon _0 a}\)

(c) \(\frac {\sqrt {2}q}{\pi \epsilon _ 0 a}\)

(d) \(\frac {q^2}{\pi \epsilon_0 a}\)

(iii) Two points A and B are located in diametrically opposite directions of a point charge of +2 μC at distances 2 m and 1 m respectively from it. The potential difference between A and B is

(a) 3 x 10³ V 

(b) 6 x 10⁴ V 

(c) -9 x 10³ V 

(d) -3 x 10³ V

OR 

Two point charges A = +3 nC and B = +1 nC are placed 5 cm apart in air. The work done to move charge B towards A by 1 cm is

(a) 2.0 × 10^-7 J 

(b) 1.35 × 10^-7 J 

(c) 2.7 × 10^-7 J 

(d) 12.1 × 10^-7 J

(iv) A charge Q is placed at the origin. The electric potential due to this charge at a given point in space is V. The work done by an external force in bringing another charge q from infinity up to the point is 

(a) V/q 

(b) V_q 

(c) V + q 

(d) V

Answer 1

(i) (c) –ke² /2 

(ii) (b) \(\frac{\sqrt {2}q^2}{\pi \epsilon _0 a}\)

Potential at the centre of the square due to four equal charges q at four corners

(iii) (c) -9 x 10³ V 

Here, q = 2 μC = 2 × 10^-6 C, r_A = 2 m, r_B = 1 m

OR

(b) 1.35 × 10^-7 J 

Required work done = Change in potential energy of the system

(iv) (b) V_q 

Work done by an external force in bringing another charge q from infinity up to the point is V_q.