Question

Four point charges \( -Q, -2Q, 2q \) and \( 4q \) are placed, one at each corner of the square. The relation between \( Q \) and \( q \) for which the potential at the centre of the square is zero is:

• A. \( Q = -q \)
• B. \( Q = \dfrac{1}{q} \)
• C. \( Q = q \)
• D. \( Q = -2q \)

Hint:

When charges are placed at the corners of a square, the potential at the center is zero when the charges are balanced such that their potentials cancel out.

Answer 1

The Correct Option is C

Step 1: The potential at the center of the square due to a point charge is given by \( V = \dfrac{kq}{r} \), where \( k \) is the Coulomb constant and \( r \) is the distance from the charge.
Step 2: For the potential at the center of the square to be zero, the sum of the potentials due to each charge must be zero. Solving this gives the relationship \( Q = q \).

Final Answer: \[ \boxed{Q = q} \]