Question

What is the direction of the electric field at the centre \(O\) of the square in the figure shown below? Given that, \( q = 10\,\text{nC} \) and the side of the square is \(5\,\text{cm}\).

• A. at \(45^\circ\) to OA upward
• B. at \(135^\circ\) to OA towards BD
• C. no direction, because \(E = 0\)
• D. None of the above

Hint:

In asymmetric charge configurations, resolve components instead of assuming cancellation.

Answer 1

The Correct Option is A

Concept: Electric field at centre due to each charge is along the line joining the charge and centre.

Step 1: Charges
\[ A(+q),\; B(-2q),\; C(-q),\; D(+2q) \]

Step 2: Directions of fields

• Positive charge → field away from charge
• Negative charge → field towards charge

Step 3: Vector addition
Resolve all four contributions: - Fields from opposite corners do not completely cancel due to unequal magnitudes - Net resultant points in upward diagonal direction

Step 4: Final direction
Resultant electric field is along a direction making \(45^\circ\) with OA upward. \[ \therefore \text{Answer is (A)} \]