In which orientation of a magnetic dipole with respect to an external…

The correct answer is Option (4) → \( \theta=0^\circ \)

A magnetic dipole of moment \( m \) at an angle \( \theta \) to a uniform field \( B \) feels a torque \( \tau=mB\sin\theta \) and has potential energy \( U_m=-mB\cos\theta \). The most stable orientation is the one of minimum potential energy.

Option (1) \( \theta=180^\circ \) — Incorrect. The torque is zero here, but \( U_m=+mB \) is the maximum. So this is the most unstable position. A slight turn makes the torque swing the dipole further away.

Option (2) \( \theta=45^\circ \) — Incorrect. The torque \( mB\sin45^\circ \) is not zero. So the dipole is not in equilibrium, and it turns towards the field.

Option (3) \( \theta=90^\circ \) — Incorrect. The torque \( mB\sin90^\circ=mB \) is the largest here, so the dipole cannot stay in this position.

Option (4) \( \theta=0^\circ \) — Correct. With the dipole along the field the torque is zero and \( U_m=-mB \) is the minimum. Any small turn raises the energy, and the torque brings the dipole back.

NCERT (2026-27):
The Dipole in a Uniform Magnetic Field – “… Equation (5.3) shows that potential energy is minimum (= –mB) at θ = 0° (most stable position) and maximum (= +mB) at θ = 180° (most unstable position).”

    \( U_m=-mB\cos\theta=-\mathbf{m}\cdot\mathbf{B} \qquad (5.3) \)