Torque on Current Loop Calculator

A current loop in a uniform magnetic field is a magnetic dipole. For N turns, area A, current I, in field B, the torque magnitude is τ = NIAB sin θ, where θ is the angle between the magnetic dipole moment μ (normal to the loop) and B.

The dipole moment vector has magnitude μ = NIA and direction given by the right-hand rule for the circulating current. Vector form: τ⃗ = μ⃗ × B⃗. Maximum torque τ_max = NIAB occurs at θ = 90° (plane of coil parallel to B). Zero torque at θ = 0° when the normal aligns with B.

Potential energy of a dipole in a field is U = −μ⃗·B⃗ = −μB cos θ. Stable equilibrium at θ = 0 (μ parallel B); unstable at θ = 180°. A compass needle is a magnetic dipole aligning with Earth's field.

DC motors exploit torque on a multi-turn coil. A split-ring commutator reverses current every half rotation so torque always aids the same spin direction. Without it, the coil would oscillate about equilibrium instead of continuous rotation.

Galvanometers use a coil in a radial B field so τ = NIAB is constant for small deflections; pointer angle measures current. Moving-coil meters are sensitive and linear for small angles.

Example: N = 50, I = 2 A, A = 0.01 m², B = 0.5 T, θ = 30° gives τ = 50×2×0.01×0.5×0.5 = 0.25 N·m.