Potential Energy Of A Magnetic Dipole — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Potential Energy of a Magnetic Dipole Applies to any magnetic dipole (bar magnet, current carrying coil) placed in a uniform external magnetic field. Used to determine stability of equilibrium. Identify the torque acting on the dipole: τ = MB sin θ. Calculate the work done by an external agent to rotate the dipole against the field torque from angle θ₁ to θ₂: W = ∫ τ dθ. Set the lower limit (reference) at 90° where U=0. Integrate ∫(MB sin θ) dθ from 90° to θ to get U = -MB cos θ. The magnetic field B must be uniform over the region of the dipole. The zero potential energy reference is arbitrarily defined at θ = 90° (π/2 rad). Confusing stable equilibrium (θ=0, U min) with zero energy. Thinking potential energy is zero at θ=0; it is actually minimum (-MB). Confusing the formula with Torque (τ = MB sin θ) vs Energy (U = -MB cos θ). Forgetting the negative sign which indicates the bound state nature relative to the reference.