Magnetic Moment Calculator
Enter current, area and field (with angle) to compute the magnetic moment m = I·A, torque and potential energy of a current loop.
Input Data
Results
At a glance:The magnetic moment of a current loop is m = I·A (vector normal to the loop by the right-hand rule). In an external field B it feels a torque τ = m×B (magnitude τ = m·B·sinθ) that aligns m with B, and has potential energy U = −m·B·cosθ (minimum when aligned). This is the operating principle of motors and magnetic compasses; atomic moments explain magnetism of materials. This tool returns m, τ and U from current I, area A, field B and angle θ.
Formula
m = I·A
τ = m·B·sinθ
U = −m·B·cosθ
$$\mu = NIA, \quad \tau = \mu B \sin\theta, \quad U = -\mu B \cos\theta, \quad \mu_B = \frac{e\hbar}{2m_e} = 9.274\times 10^{-24}\,\text{A·m}^2$$How to Use
- Enter current I (A) and area A (m²).
- Enter field B (T) and angle θ (°).
- The calculator returns m, torque τ and potential energy U.
Case Studies
Single loop
I = 3 A, A = 0.005 m², B = 0.4 T, θ=90°.
m = 0.015 A·m², τ = 0.015×0.4 = 0.006 N·m.
Aligns with the field.
FAQ
How is this different from the multi-turn dipole calculator?
This uses a single loop m = I·A; the N-turn version multiplies by N (m = N·I·A). Same torque/energy relations apply.
When is potential energy maximum?
At θ=180° (anti-aligned), U = +mB — unstable equilibrium; the torque restores alignment.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.