Question

An electric dipole of length \(2 \text{ cm}\) is placed at \(60^{\circ}\) to a uniform electric field of \(10^{5} \text{ N/C}\). If it experiences a torque of \(9\sqrt{3} \text{ Nm}\), the magnitude of the charge is:

• A. \(7 \times 10^{-3} \text{ C}\)
• B. \(8 \times 10^{-3} \text{ C}\)
• C. \(9 \times 10^{-3} \text{ C}\)
• D. \(\frac{9}{2} \times 10^{-3} \text{ C}\)

Hint:

Always convert length to meters ($2 \text{ cm} = 0.02 \text{ m}$) before calculation.

Answer 1

The Correct Option is C

Step 1: Formula
Torque $\tau = pE \sin \theta = (q \cdot 2l) E \sin \theta$.

Step 2: Values
$9\sqrt{3} = q (0.02) (10^5) (\frac{\sqrt{3}}{2})$.

Step 3: Calculation
$9 = q (0.01) (10^5) \implies 9 = q (10^3)$.
$q = 9 \times 10^{-3} \text{ C}$.
Final Answer: (C)