A magnetic needle of moment M is kept in earth's magnetic field. If the angle between M→ and BH→ is θ, then for most unstable equilibrium configuration θ will be

Magnetic dipole in a uniform magnetic field

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Question

A magnetic needle of moment M is kept in earth's magnetic field. If the angle between $\vec{M} and \vec{B_{H}} is θ$ , then for most unstable equilibrium configuration $θ$ will be

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Solution

Potential energy $U = - \vec{M} . \vec{B_{H}} = - {MB}_{H} cosθ$
Potential energy of a system is maximum in most unstable configuration
When $θ = 180^{o}, U = - {MB}_{H} \cos 180^{o}$ , i.e., $U = + {MB}_{H}$ which is maximum.

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