Question

Four point charges -Q, -q, 2q and 2Q 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 = (1)/(q)

Hint:

When multiple charges are equidistant from a point, electric potential depends only on the algebraic sum of charges, not their positions.

Answer 1

The Correct Option is A

Step 1: The electric potential due to a point charge q at a distance r is: V = (kq)/(r)
Step 2: All four charges are placed at the corners of a square, so their distances from the centre are equal. Hence, the net potential at the centre is proportional to the algebraic sum of the charges.
Step 3: Sum of charges: (-Q) + (-q) + 2q + 2Q = Q + q
Step 4: For the potential at the centre to be zero: Q + q = 0 ⟹ Q = -q