Magnetic Torque Calculator
Enter turns, current, area and field (with angle) to compute the torque τ = N·I·A·B·sinθ on a current loop in a magnetic field.
Input Data
Results
At a glance:A current-carrying loop in a magnetic field experiences a torque that tends to align its magnetic moment m = N·I·A with the field. The torque magnitude is τ = m·B·sinθ = N·I·A·B·sinθ, where N is turns, I current, A area, B field and θ the angle between m and B. Maximum at θ=90° (τ = mB), zero when aligned (θ=0). This torque is what spins motor rotors and deflects galvanometer needles; the rotational work changes the potential energy U = −m·B·cosθ. This tool returns τ (N·m and mN·m) and m from N, I, A, B and θ.
Formula
m = N·I·A
τ = m·B·sinθ = N·I·A·B·sinθ
U = −m·B·cosθ
$$\boldsymbol{\tau} = \boldsymbol{\mu} \times \mathbf{B} = NIA B \sin\theta, \quad \boldsymbol{\mu} = NIA\,\hat{\mathbf{n}}$$How to Use
- Enter turns N, current I, area A, field B and angle θ.
- The calculator returns torque τ and magnetic moment m.
Case Studies
DC motor coil
N=200, I=1.5 A, A=0.004 m², B=0.3 T, θ=90°.
m = 1.2 A·m², τ = 1.2×0.3 = 0.36 N·m.
Spins the rotor.
FAQ
Why does the torque vanish when aligned?
At θ=0 or 180° sinθ=0, so no torque — the loop is in equilibrium. Only θ=0 (aligned) is stable (lowest U=−mB).
How does this make a motor spin?
The torque rotates the coil; a commutator reverses current each half-turn to keep torque in the same rotational direction, producing continuous rotation.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.