Question

Four point charges \(-Q\), \(-q\), \(2q\) and \(3Q\) are placed at corners of the square respectively. The relation between \(Q\) and \(q\) for which the potential at the centre of the square is zero, is

• A. \(Q=q\)
• B. \(Q=-q/2\)
• C. \(Q=-1/q\)
• D. \(Q=1/2q\)

Hint:

All charges are at the same distance from the centre, so the potential is zero when the algebraic sum of the charges is zero.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Potential is a scalar. Each corner is at the same distance \(r\) from the centre, so \(V=\dfrac{k}{r}(\text{sum of charges})\).

Step 2: Sum of charges
\(-Q-q+2q+3Q=2Q+q\)

Step 3: Calculation
\(V=0\) needs \(2Q+q=0\), so \(Q=-\dfrac{q}{2}\).

Final Answer:
The potential at the centre is zero when Q = −q/2. \[ \boxed{\text{(B) }Q=-\dfrac{q}{2}} \]