Question

Two spheres A and B having respective charges 6 C and 12 C placed at a distance \( d \) repel each other by a force \( F \). The charge given to sphere A to reverse the force as \( -F \) is:

• A. -8 C
• B. -12 C
• C. -10 C
• D. -6 C
• E. -15 C

Hint:

The force between two charges can be reversed by changing the sign of one of the charges. The magnitude of the force remains the same, but the direction is reversed.

Answer 1

The Correct Option is B

The force between two charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by Coulomb's law: \[ F = k \frac{|q_1 q_2|}{r^2} \] where: - \( k \) is Coulomb's constant,
- \( r \) is the distance between the charges.
For the charges on spheres A and B, we are given:
- \( q_1 = 6 \, {C} \),
- \( q_2 = 12 \, {C} \),
- The force between them is \( F \).
Now, we are asked to find the charge \( q_1' \) that must be given to sphere A in order to reverse the direction of the force to \( -F \). 
The charges should attract each other instead of repelling, meaning the product of the charges should become negative.
To reverse the force direction, the charge \( q_1' \) on sphere A must be: \[ q_1' = -12 \, {C} \] Thus, the charge to be given to sphere A to reverse the force is \( -12 \, {C} \). Therefore, the correct answer is: \[ \boxed{-12 \, {C}} \]