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]

January 14, 2024

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 = (4πε_o)(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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