JEE Main 2025 — Electrostatics Question with Solution

Given:

Potential difference $V=5\text{V}$

Separation between the plates $d=0.5\text{mm}=0.5\times 10^{-3}\text{m}$

The electric field $E$ is calculated as:

$E=\frac{V}{d}=\frac{5}{0.5\times 10^{-3}}=10^4\text{V/m}$

The torque $\tau$ experienced by the dipole in the electric field is given by:

$\tau =PE\sin \theta$

Where:

$P$ is the dipole moment,

$E$ is the electric field,

$\theta =30^{\circ }$ is the angle of rotation.

The dipole moment $P$ is calculated by:

$P=q\times a=(2\times 10^{-6}\text{C})\times (0.5\times 10^{-6}\text{m})=1\times 10^{-12}\text{C}\cdot \text{m}$

Substituting the values into the torque equation:

$\tau =(1\times 10^{-12}\text{C}\cdot \text{m})\times 10^4\text{V/m}\times \sin 30^{\circ }$

Since $\sin 30^{\circ }=0.5$, the torque simplifies to:

$\tau =1\times 10^{-12}\times 10^4\times 0.5=5\times 10^{-9}\text{N}\cdot \text{m}$

Thus, the torque is $5\times 10^{-9}\text{N}\cdot \text{m}$.