Question

Two identical conducting spheres, one carrying a charge of +4q and the other carrying -2q, are kept at a distance r apart in a vacuum. The magnitude of the electrostatic force between them is F. If they are brought into contact and then separated to the same distance r, what is the new electrostatic force between them?

• A. F/8
• B. F/4
• C. F
• D. F/2

Hint:

For problems involving charge redistribution on identical conducting spheres, remember that the total charge is conserved and distributes equally. The magnitude of force from Coulomb's law uses the absolute value of the product of charges.

Answer 1

The Correct Option is A

Step 1: When identical conducting spheres touch, the total charge \( 4q + (-2q) = 2q \) is shared equally, so each sphere carries \( q \) afterwards.

Step 2: The force is proportional to the product of the charges: originally proportional to \( |4q\times(-2q)| = 8q^2 \), and afterwards proportional to \( q\times q = q^2 \).

Step 3: Ratio of new to old force is \( \frac{q^2}{8q^2} = \frac{1}{8} \).
\[ \boxed{F' = \dfrac{F}{8}} \]