Magnetic Dipole Moment Calculator
Enter turns, current and area (with field angle) to compute the magnetic dipole moment m = N·I·A, its torque and potential energy.
Input Data
Results
At a glance:The magnetic dipole moment of a planar current loop is m = N·I·A (vector normal to the loop by the right-hand rule), where N is turns, I current and A area. In an external field B it experiences a torque τ = m×B with magnitude τ = m·B·sinθ (θ angle between m and B) that aligns m with B, and potential energy U = −m·B·cosθ (minimum when aligned). This is the basis of electric motors, galvanometers and compass needles; atomic moments explain paramagnetism. This tool returns m, τ and U from N, I, A, B and θ.
Formula
m = N·I·A
τ = m·B·sinθ
U = −m·B·cosθ
$$\mu = NIA, \quad \tau = \mu B \sin\theta$$$$U = -\mu B \cos\theta$$How to Use
- Enter turns N, current I and area A.
- Enter the field B and angle θ.
- The calculator returns m, torque τ and potential energy U.
Case Studies
Motor coil
N=100, I=2 A, A=0.01 m², B=0.5 T, θ=90°.
m = 2 A·m², τ = 2×0.5×1 = 1 N·m.
Rotates the coil toward alignment.
FAQ
Why does a loop feel a torque in a field?
Opposite sides of the loop carry opposite currents, so the field pushes them in opposite directions, creating a couple that rotates m toward alignment with B (lowest energy).
When is the energy lowest?
U = −mB cosθ is minimum at θ=0 (m parallel to B, U=−mB) and maximum at θ=180° (anti-parallel). The torque is zero at both but stable only at alignment.
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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.