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.
$2a=2\times 10^{-2}cm=2\times 10^{-4}m$

$\therefore$ Electric dipole moment, $p=q\times 2a$
$=4\times 10^{-8}\times 2\times 10^{-4}=8\times 10^{-12}C-m$
$\therefore$ Maximum torque $\left(\theta =90^{\circ }\right)$ is given as,
${\tau }_{\max }=pE\sin 90^{\circ }=pE$
$=8\times 10^{-12}\times 4\times 10^8=32\times 10^{-4}N-m$
Work done in rotating through $180^{\circ }$ is given as
$W=pE\left(\cos {\theta }_1-\cos {\theta }_2\right)$
$=8\times 10^{-12}\times 4\times 10^8\left(\cos 0^{\circ }-\cos 180^{\circ }\right)$
$=64\times 10^{-4}J$