Question

Point charges \(-3Q, -q, 2q\) and \(2Q\) are placed, one at each corner of a square. The relation between \(Q\) and \(q\) for which the potential at the centre of the square is zero is

• A. \( Q = \frac{q}{4} \)
• B. \( Q = -q \)
• C. \( Q = -\frac{q}{4} \)
• D. \( Q = q \)

Hint:

At centre of square, all distances are equal, so potential depends only on algebraic sum of charges.

Answer 1

The Correct Option is D

Step 1: Expression for electric potential.
Electric potential due to a point charge is:
\[ V = \frac{kq}{r} \]

Step 2: Same distance from centre.
All charges are placed at corners of a square, so distance of each charge from centre is same.
Thus, total potential is proportional to algebraic sum of charges.

Step 3: Write total potential.
\[ V \propto (-3Q) + (-q) + (2q) + (2Q) \]

Step 4: Simplify expression.
\[ V \propto (-3Q + 2Q) + (-q + 2q) \] \[ V \propto -Q + q \]

Step 5: Condition for zero potential.
\[ -Q + q = 0 \]

Step 6: Solve for relation.
\[ Q = q \]

Step 7: Final conclusion.
\[ \boxed{Q = q} \] Hence, correct answer is option (D).