JEE Main 2025 — Magnetic Properties Of Matter Question with Solution

To determine the potential energy of a magnetic dipole in a uniform magnetic field, we start with the torque equation:

$\tau =M\times B=MB\sin 60^{\circ }$

Given that $\tau =80\sqrt{3}\text{N m}$ and $\sin 60^{\circ }=\frac{\sqrt{3}}{2}$, we can equate and solve for $MB$:

$MB\frac{\sqrt{3}}{2}=80\sqrt{3}$

Solving for $MB$, we find:

$MB=160$

The potential energy $U$ of the dipole in the magnetic field is given by:

$U=-M\cdot B=-MB\cos 60^{\circ }$

Substituting in $\cos 60^{\circ }=\frac{1}{2}$, we calculate:

$U=-160\times \frac{1}{2}=-80\text{J}$

Thus, the potential energy of the dipole is $-80\text{J}$.