Question

The sum of two point charges is 7µ C. They repel each other with a force of 1 N when kept 30cm apart in free space. Calculate the value of each charge.  [CBSE (F) 2009]

  • AAAAAAAAAAAAAA Electrostatics
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Answer

q1 + q2 = 7µ —- (i)

F = {1\over 4 \pi\varepsilon_0}{q_1q_2\over r^2} {1\over 4 \pi\varepsilon_0}{q_1q_2\over r^2}=1

or, q1 q2 = (4πεo)(0.30)2

or, q1 q2 = 10-11 —- (ii)

(q1 – q2)2 = (q1 + q2)2 – 4q1 q2

= (7µ)2 – 4×10-11

= 49 × 10-12 – 40×10-12

or, (q1 – q2)2 = 9 × 10-12

or, q1 – q2 = 3 × 10-6 —- (iii)

Solving (i) and (iii), we get

q1 = 5 × 10-6 C = 5µ and q2 = 7µ – 5µ = 2 µC

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