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Magnetic Effects & Magnetism

JEE Main level, single correct, medium

232 of 276

Question 232 of 276

A rectangular loop of sides $10cm$ and $5cm$ , carrying a current $I$ of $12A$ , is placed in different orientations as shown in the figure below.
(a) (b)

(c) (d)
If there is a uniform magnetic field of $0.3T$ in the positive $z$ direction, in which orientations the loop would be in $(i)$ stable equilibrium and $(ii)$ unstable equilibrium?

Show answer and solution

Answer: (D) (b) and (d), respectively.

For a magnetic dipole placed in a uniform magnetic field, the torque is given by

\vec{\tau }=\vec{M}\times \vec{B}

, and potential energy

U

is given as,

U=-\vec{M}\cdot \vec{B}=-MB\cos \theta

When

\vec{M}

is in the same direction as

\vec{B}

then

\vec{\tau }=0

and

U

is minimum =

-MB

\theta ={0}^{o}

\Rightarrow

Stable equilibrium is (b).
When

\vec{M}

the opposite direction of

\vec{B}

, then

\vec{\tau }=0

and

U

is max =

+MB

As,

\theta ={180}^{o}

\Rightarrow

Unstable equilibrium in (d)

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JEE Main 2025 Apr 2 Shift 1 question paper

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