Question

Two opposite and equal charges $4 \times 10^{-8}$ coulomb when placed $2 \times 10^{-2} cm$ away, form a dipole. If this dipole is placed in an external electric field $4 \times 10^{8}$ newton/ coulomb, the value of maximum torque and the work done in rotating it through $180^{\circ}$ will be

• A. $64 \times 10^{-4} Nm$ and $64 \times 10^{-4} J$
• B. $32 \times 10^{-4} Nm$ and $32 \times 10^{-4} J$
• C. $64 \times 10^{-4} Nm$ and $32 \times 10^{-4} J$
• D. $32 \times 10^{-4} Nm$ and $64 \times 10^{-4} J$

Answer 1

Answer: (D)

Dipole moment $p=4 \times 10^{-8} \times 2 \times 10^{-4}$
$=8 \times 10^{-12} m$
Maximum torque $=p E=8 \times 10^{-12} \times 4 \times 10^{8}$
$=32 \times 10^{-4} Nm$
Work done in rotating through $180^{\circ}=2\, p E$
$=2 \times 32 \times 10^{-4}=64 \times 10^{-4} J$