Question

The force between two spheres with charges +7 $ \mu C $ and -5 $ \mu C $ is F. If each sphere is given an additional charge of +2 $ \mu C $, the new force of attraction will be

• A. \( \frac{F}{2} \)
• B. \( \frac{F}{\sqrt{3}} \)
• C. \( F \)
• D. \( 2F \)

Hint:

When charges are changed, the force between them changes proportionally to the product of the charges.

Answer 1

The Correct Option is D

The force between two charges is given by Coulomb's law: \[ F = k \frac{|q_1 q_2|}{r^2} \] where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between them. After adding \( +2 \, \mu C \) to both spheres, the new charges are: \[ q_1 = +7 \, \mu C + 2 \, \mu C = +9 \, \mu C, \quad q_2 = -5 \, \mu C + 2 \, \mu C = -3 \, \mu C \]
Thus, the new force \( F' \) is: \[ F' = k \frac{|9 \, \mu C \times (-3) \, \mu C|}{r^2} = 2F \]
Thus, the new force is \( 2F \).