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Current-Loop Magnetic Dipole Moment Calculator — result sheet
Calculate the magnetic dipole moment of a multi-turn current loop and its ideal torque and potential energy in a uniform magnetic field.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Magnetic moment μ = NIA; torque magnitude τ = μB sin(θ); dipole potential energy U = −μB cos(θ).
A current loop behaves as a magnetic dipole in the ideal uniform-field model. The magnetic moment is proportional to turns, current, and the area of one turn; the field then produces a torque that depends on the angle between the moment and field. Potential energy is included to show the orientation convention. The calculator does not model a nonuniform field, coil geometry beyond area and turns, inductance, resistance, heating, ferromagnetic cores, or motor performance.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Loop current — A; minimum 1.0E-6; maximum 1000000
- Area of one loop — m²; minimum 1.0E-6; maximum 1000000
- Number of turns — turns; minimum 1.0E-6; maximum 1000000
- Uniform magnetic field — T; minimum 1.0E-6; maximum 1000000
- Angle between moment and field — °; minimum 0; maximum 180
Worked example
| Input | Value |
|---|---|
| Loop current | 2 |
| Area of one loop | 0.03 |
| Number of turns | 20 |
| Uniform magnetic field | 0.4 |
| Angle between moment and field | 60 |
The loop has μ = 1.2 A·m², ideal torque about 0.4157 N·m, and dipole energy −0.24 J.
Assumptions and limits
- The loop current, area, turns, and field magnitude are positive finite quantities.
- The current is steady and the loop is represented by a single effective area per turn.
- The magnetic field is uniform over the loop and the dipole approximation is used.
- The angle is measured between the magnetic-moment vector and field vector in degrees.
- Torque is reported as a magnitude while energy uses the signed cosine convention.
- Core permeability, field gradients, self-inductance, resistance, heating, and mechanical constraints are excluded.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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