Question

Two charged spheres of \( -20\, \mu\text{C} \) and \( 60\, \mu\text{C} \) are kept at a certain distance. They are touched and kept again at the same distance. What is the ratio of force experienced before and after?

• A. \( 1 : 3 \)
• B. \( 3 : 1 \)
• C. \( 2 : 1 \)
• D. \( 1 : 2 \)

Hint:

After touching, charges redistribute equally on identical conductors. Use Coulomb’s law before and after.

Answer 1

The Correct Option is B

Before touching: \[ F_1 = k \cdot \frac{|-20 \cdot 60| \times 10^{-12}}{r^2} = \frac{1200k}{r^2} \] After touching, total charge = \( 60 - 20 = 40\, \mu\text{C} \)
Shared equally: each gets \( 20\, \mu\text{C} \)
\[ F_2 = k \cdot \frac{(20)^2 \times 10^{-12}}{r^2} = \frac{400k}{r^2} \] Ratio: \[ \frac{F_1}{F_2} = \frac{1200}{400} = 3:1 \]