Magnetic Dipole Moment
m = N · I · A
Quick answer
This calculator solves m = N × I × A for Dipole Moment. With Number of Turns 0.5, Current 2 A, Loop Area 10 cm², the result is 1 mA·m². It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The magnetic dipole moment of a current loop measures the strength of the equivalent bar magnet it forms. It equals the number of turns times the current times the enclosed area. The torque a loop feels in an external field is τ = m × B, so the dipole moment sets the torque available in motors, galvanometers, and compass needles.
Variables
- m — Magnetic dipole moment (A·m²)
- N — Number of turns
- I — Loop current (A)
- A — Area enclosed by the loop (m²)
Practical Notes
Torque in an external field is τ = m·B·sinθ, and the loop’s potential energy is −m·B·cosθ. Larger area or more turns gives more torque for the same current.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| m | Dipole Moment | A·m² | A·m², mA·m² |
| N | Number of Turns | — | — |
| I | Current | A | pA, nA, µA, mA, A, kA |
| A | Loop Area | cm² | mm², cm², m² |
Step by step
- 1. What you know: Number of Turns 0.5, Current 2 A, Loop Area 10 cm²
- 2. The relation: m = N × I × A
- 3. Substitute: N = 0.5, I = 2 A, A = 10 cm²
- 4. Result: Dipole Moment = 1 mA·m²
Worked examples
Minimum range
Given: Number of Turns 0.025, Current 2 mA, Loop Area 10 mm²
Result: Dipole Moment = 5 × 10⁻⁷ mA·m²
Low range
Given: Number of Turns 0.25, Current 20 mA, Loop Area 1 cm²
Result: Dipole Moment = 5 × 10⁻⁴ mA·m²
Typical
Given: Number of Turns 0.5, Current 2 A, Loop Area 10 cm²
Result: Dipole Moment = 1 mA·m²
High range
Given: Number of Turns 0.8, Current 100 A, Loop Area 100 cm²
Result: Dipole Moment = 0.8 A·m²
Maximum range
Given: Number of Turns 8, Current 1 kA, Loop Area 0.1 m²
Result: Dipole Moment = 800 A·m²
Solving for each variable
Solve for Dipole Moment
Number of Turns 0.025, Current 2 mA, Loop Area 10 mm² → 5 × 10⁻⁷ mA·m²
Solve for Number of Turns
Dipole Moment 0.1 mA·m², Current 2 mA, Loop Area 10 mm² → 5000
Solve for Current
Dipole Moment 0.1 mA·m², Number of Turns 0.025, Loop Area 10 mm² → 0.4 kA
Solve for Loop Area
Dipole Moment 0.1 mA·m², Number of Turns 0.025, Current 2 mA → 2 m²
How Dipole Moment changes with Number of Turns
| Number of Turns (input) | Dipole Moment (result) |
|---|---|
| 0.05 | 0.1 mA·m² |
| 0.125 | 0.25 mA·m² |
| 0.25 | 0.5 mA·m² |
| 0.375 | 0.75 mA·m² |
| 0.5 | 1 mA·m² |
| 0.75 | 1.5 mA·m² |
| 1 | 2 mA·m² |
| 2 | 4 mA·m² |
| 3.5 | 7 mA·m² |
| 5 | 10 mA·m² |
The same result in other units
| Unit | Value |
|---|---|
| A·m² | 0.001 |
| mA·m² | 1 |
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<p><a href="https://vbatpower.com/formulas/magnetic-dipole-moment/">Magnetic Dipole Moment</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Magnetic Dipole Moment?
Use m = N × I × A. With Number of Turns 0.5, Current 2 A, Loop Area 10 cm², Dipole Moment works out to 1 mA·m².
What is the formula for Magnetic Dipole Moment?
The formula is m = N × I × A. The magnetic dipole moment of a current loop measures the strength of the equivalent bar magnet it forms.
How do you find Number of Turns when you know the other values?
Rearrange for Number of Turns: with Dipole Moment 0.1 mA·m², Current 2 mA, Loop Area 10 mm², Number of Turns is 5000.
How do you find Current when you know the other values?
Rearrange for Current: with Dipole Moment 0.1 mA·m², Number of Turns 0.025, Loop Area 10 mm², Current is 0.4 kA.
What units does Magnetic Dipole Moment use?
Dipole Moment is shown in A·m², mA·m². Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Fields & Electromagnetism formulas →Need more features?
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