Question

An electric dipole of length \(3\text{cm}\) is placed with its axis making an angle of \(60^{\circ}\) with a uniform electric field of \(5\times 10^4\) N/C. It experiences a torque of \(9\sqrt{3}\) Nm. The magnitude of charge on the dipole is \((sin60^{\circ} = \frac{\sqrt{3}}{2})\)

• A. \(0.6\times 10^{-2}\) C
• B. \(1.2\times 10^{-2}\) C
• C. \(1.8\times 10^{-2}\) C
• D. \(2.4\times 10^{-2}\) C

Hint:

Torque \(\tau=pE\sin\theta\) with \(p=q\times2l\) (the dipole length).

Answer 1

The Correct Option is B

Step 1: Find the dipole moment
$p=\dfrac{\tau}{E\sin\theta}=\dfrac{9\sqrt3}{5\times10^4\times\sqrt3/2}=3.6\times10^{-4}$ C m.

Step 2: Divide by the length
$q=\dfrac{p}{\ell}=\dfrac{3.6\times10^{-4}}{0.03}=1.2\times10^{-2}$ C, option (B).

Final Answer:
The charge is $1.2\times10^{-2}$ C, option (B). \[ \boxed{1.2\times10^{-2}\ \text{C}} \]