Question

An electric dipole is placed in an uniform electric field of magnitude $40\text{N/C}$. The graph given below represents the magnitude of the torque on dipole versus the angle $\theta$ between field and dipole moment. The magnitude of dipole moment is equal to

• A. $2\times {10}^{-25}\text{C-m}$
• B. $1.25\times {10}^{-28}\text{C-m}$
• C. $2.5\times {10}^{-28}\text{C-m}$
• D. $5.0\times {10}^{-28}\text{C-m}$

Answer 1

The correct option is B $1.25\times {10}^{-28}\text{C-m}$

Given:
${\tau }_{max}=50\times {10}^{-28}\text{N-m}$
$E=40\text{N/C}$

From the graph of $|\tau |$ vs $\theta$, maximum magnitude of torque is
${\tau }_{max}=50\times {10}^{-28}\text{N-m}$

Since,
$\overrightarrow{\tau }=\overrightarrow{p}\times \overrightarrow{E}$
$\Rightarrow |\overrightarrow{\tau }|=pE\sin \theta$

For maximum magnitude of torque,
$\theta ={90}^{\circ }\to \sin \theta =1$

Thus, ${\tau }_{max}=pE$

$\Rightarrow 50\times {10}^{-28}=p\times 40$

$\Rightarrow p=\frac{50}{40}\times {10}^{-28}$

$\therefore p=1.25\times {10}^{-28}\text{C-m}$

Hence, option $\left(b\right)$ is correct.