Magnetic Dipole Moment Calculator
Free calculate magnetic dipole moment from current, loop area, and number of turns. Get instant, accurate results with our easy-to-use calculator.
Input Parameters
1 for single loop, >1 for coil/solenoid
Results
Enter parameters to calculate
What is Magnetic Dipole Moment?
The magnetic dipole moment (μ) is a vector quantity that characterizes the strength and orientation of a magnetic dipole, such as a current-carrying loop. It determines how the loop interacts with external magnetic fields.
For a current loop, the magnetic dipole moment is μ = N × I × A, where N is the number of turns, I is the current, and A is the loop area. The direction is perpendicular to the loop plane, determined by the right-hand rule.
Magnetic dipole moments are fundamental in understanding electromagnets, motors, generators, and magnetic materials. They determine the torque a magnetic field exerts on a current loop and the magnetic field the loop produces.
Magnetic Dipole Moment Formula
Where:
- • μ = Magnetic dipole moment (A·m²)
- • N = Number of turns
- • I = Current (A)
- • A = Loop area (m²)
For circular loop: A = πr²
For rectangular loop: A = length × width
Direction: Perpendicular to loop plane (right-hand rule)
How to Calculate
-
1
Convert all units to SI
Convert current to amperes, dimensions to meters, area to m².
-
2
Calculate loop area
Circular: A = πr². Rectangular: A = length × width. Or use direct area input.
-
3
Calculate magnetic moment
μ = N × I × A. Multiply number of turns, current, and area.
Practical Examples
Example 1: Circular Loop
Radius: 0.10 m, Current: 5.00 A, Single turn (N=1).
Solution:
A = π × (0.10)² = 0.0314 m²
μ = 1 × 5.00 × 0.0314
μ = 0.157 A·m²
Example 2: Coil
Same loop but with 100 turns (N=100).
Solution:
μ = 100 × 5.00 × 0.0314
μ = 15.7 A·m² (100× larger!)
Applications
Electromagnets
Designing electromagnets, calculating magnetic field strength, and determining force/torque on magnetic materials.
Motors & Generators
Understanding torque in electric motors, analyzing generator output, and designing electromagnetic devices.
Magnetic Materials
Characterizing permanent magnets, understanding magnetic domains, and analyzing magnetic properties of materials.
Education
Teaching electromagnetism, understanding magnetic fields, and learning about current loops and dipoles.
Frequently Asked Questions
What is the direction of magnetic dipole moment?
Use the right-hand rule: curl fingers in direction of current flow around loop. Thumb points in direction of μ (perpendicular to loop plane).
How does number of turns affect the moment?
Magnetic moment is directly proportional to number of turns: μ ∝ N. Doubling turns doubles the moment. This is why coils are used instead of single loops.
What is the torque on a magnetic dipole?
τ = μ × B (cross product). Maximum torque when μ ⟂ B. In uniform field: τ = μB sin(θ), where θ is angle between μ and B.
Can this formula be used for permanent magnets?
The formula μ = NIA is for current loops. Permanent magnets have intrinsic magnetic moments from atomic electron spins/orbits, but the concept is similar.
What is the energy of a magnetic dipole in a field?
U = -μ·B = -μB cos(θ). Minimum energy when μ and B are parallel. This energy difference causes the torque that aligns the dipole with the field.