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

Question

Two opposite and equal charges each of magnitude $4 \times 10^{-8} \mathrm{C}$ form a dipole. Their separation is $2 \times 10^{-2} \mathrm{~cm}$. When this dipole is placed in an external electric field $4 \times 10^8 \mathrm{NC}^{-1}$, then the value of maximum torque and the work done in rotating it through $180^{\circ}$ respectively will be, $64 \times 10^{-4} \mathrm{Nm}$ and $64 \times 10^{-4} \mathrm{~J}$, $32 \times 10^{-4} \mathrm{Nm}$ and $32 \times 10^{-4} \mathrm{~J}$, $64 \times 10^{-4} \mathrm{Nm}$ and $32 \times 10^{-4} \mathrm{~J}$, $32 \times 10^{-4} \mathrm{Nm}$ and $64 \times 10^{-4} \mathrm{~J}$

MARKS App · Accepted Answer

Separation between the electric dipole. $2 a=2 \times 10^{-2} \mathrm{~cm}=2 \times 10^{-4} \mathrm{~m}$ $\therefore$ Electric dipole moment, $p=q \times 2 a$ $=4 \times 10^{-8} \times 2 \times 10^{-4}=8 \times 10^{-12} \mathrm{C}-\mathrm{m}$ $\therefore$ Maximum torque $\left(\theta=90^{\circ}\right)$ is given as, $\begin{aligned} \tau_{\max } & =p E \sin 90^{\circ}=p E \ & =8 \times 10^{-12} \times 4 \times 10^8=32 \times 10^{-4} \mathrm{~N}-\mathrm{m} \end{aligned}$ Work done in rotating through $180^{\circ}$ is given as $\begin{aligned} W & =p E\left(\cos \theta_1-\cos \theta_2\right) \ & =8 \times 10^{-12} \times 4 \times 10^8\left(\cos 0^{\circ}-\cos 180^{\circ}\right) \ & =64 \times 10^{-4} \mathrm{~J} \end{aligned}$

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