Question

Two point charges $-4\mu C$ and $+4\mu C$ are placed at points A$(1,0,4)$ and B$(2,-1,5)$ located in an electric field $\overrightarrow{E}=0.20\hat{i}V/cm$ . The magnitude of torque acting on the dipole is

• A. $8\times {10}^{-5}N-m$
• B. $\frac{8}{\sqrt{2}}\times {10}^{-5}N-m$
• C. $8\sqrt{2}\times {10}^{-5}N-m$
• D. $2\sqrt{2}\times {10}^{-5}N-m$

Answer 1

The correct option is C $8\sqrt{2}\times {10}^{-5}N-m$

Torque acting on the dipole, $\overrightarrow{\tau }=\overrightarrow{P}\times \overrightarrow{E}=q\left(2\overrightarrow{a}\right)\times \overrightarrow{E}$
Here, separation between the charges, $2\overrightarrow{a}=(2-1)\hat{i}+(-1-0)\hat{j}+(5-4)\hat{k}$
$=\hat{i}-\hat{j}+\hat{k}$
Electric field, $\overrightarrow{E}=0.20\hat{i}V/cm=20\hat{i}V/m$
$\therefore \overrightarrow{\tau }=(4\times {10}^{-6})\left[\right(\hat{i}-\hat{j}+\hat{k})\times 20\hat{i}]$
$\overrightarrow{\tau }=8\times {10}^{-5}(\hat{k}+\hat{j})$
Magnitude of torque, $\tau =\sqrt{(8\times {10}^{-5}{)}^2+(8\times {10}^{-5}{)}^2}\Rightarrow \tau =8\sqrt{2}\times {10}^{-5}N-m$