Question

Charges \(q\), \(2q\), \(3q\) and \(4q\) are placed at the corners \(A\), \(B\), \(C\) and \(D\) respectively of a square as shown in the figure. The direction of electric field at the centre \(O\) of the square is along

• A. AB
• B. CB
• C. BD
• D. AC \bigskip

Hint:

When charges are placed at the corners of a square, first combine the electric fields due to opposite corners along each diagonal. Then add the two diagonal resultants using symmetry and vector addition.

Answer 1

The Correct Option is B

Concept: Electric field at centre due to each charge is proportional to charge magnitude and directed radially. Find net field by vector addition of opposite corner contributions.

Step 1: Pair opposite corners: AC has +3q and -q, net field along diagonal proportional to 2q towards -q. BD has +4q and -2q, net field proportional to 2q towards -2q.

Step 2: Both diagonal fields have magnitude \(E_0\). Components: AC field = \((-\sqrt2 E_0, -\sqrt2 E_0)\), BD field = \((\sqrt2 E_0, -\sqrt2 E_0)\). Sum = \((0, -2\sqrt2 E_0)\), direction vertically downward, parallel to side CB.

Step 3: Write the final answer. \(\boxed{\text{Direction of electric field is along }CB}\)