Question

Two opposite and equal charges each of magnitude $4 \times 10^{-8} C$ form a dipole. Their separation is $2 \times 10^{-2} cm$. When this dipole is placed in an external electric field $4 \times 10^{8} N \cdot C ^{-1}$, the value of maximum torque and the work done in rotating it through $180^{\circ}$ respectively, will be

• A. $64 \times 10^{-4} N \cdot m \& 64 \times 10^{-4} J$
• B. $32 \times 10^{-4} N . m \& 32 \times 10^{-4} J$
• C. $64 \times 10^{-4} N . m \& 32 \times 10^{-4} J$
• D. $32 \times 10^{-4} N \cdot m \& 64 \times 10^{-4} J$

Answer 1

Answer: (D)

Separation between the electric dipole.
$2 a=2 \times 10^{-2} cm =2 \times 10^{-4} m$

$\therefore $ Electric dipole moment, $p=q \times 2 a$
$=4 \times 10^{-8} \times 2 \times 10^{-4}=8 \times 10^{-12} C - m$
$\therefore $ Maximum torque $\left(\theta=90^{\circ}\right)$ is given as,
$\tau_{\max }=p E \sin 90^{\circ}=p E$
$=8 \times 10^{-12} \times 4 \times 10^{8}=32 \times 10^{-4} N - m$
Work done in rotating through $180^{\circ}$ is given as
$W=p E\left(\cos \theta_{1}-\cos \theta_{2}\right)$
$=8 \times 10^{-12} \times 4 \times 10^{8}\left(\cos 0^{\circ}-\cos 180^{\circ}\right)$
$=64 \times 10^{-4} J$