Question

Two point charges which are 10 cm apart repel each other with a force of 18N. If the sum of the charges is 9 μC, the charges are________
1. 5μC , -­4μ C
2. -5μC, ­-4μC
3. 5μC, 4μC
4. -5μC, 4μC

Answer 1

Correct Answer - Option 3 : 5μC, 4μC

CONCEPT:

• Electrostatic Force: between two charges q1 and q2 at the distance of R is given by:

\(F=\frac{1}{4\pi ϵ_0}\frac{q_1q_2}{R^2} \)

where F is the electrostatic force, q1 and q2 are the charges, and ϵ0 is the electrical permittivity of the vacuum.

CALCULATION:

Given that F = 18N; R = 10cm = 0.1m;

q₁ + q₂ = 9μC.................(i)

We know \(F=\frac{1}{4\pi ϵ_0}\frac{q_1q_2}{R^2} \)

\(18=9×10^9×\frac{q_1q_2}{0.1^2} \)

q1.q2 = 2 × 10^-11.................(ii)

From identity (a - b)² = (a+b)² - 4ab

eq (i) and eq (ii)

q1 - q2 = 1μC...............(iii)

from eq (i) and (iii)

q1 = 5μC and q2 = 4μC

So the correct answer is option 3.