Calculator inputs
Example data table
Example values below use dipole moment = 0.8 A·m², magnetic length = 0.10 m, and relative permeability = 1.
| Case | Distance (m) | Model | Field line | Field (T) | Field (µT) | Field (Gauss) |
|---|---|---|---|---|---|---|
| Example 1 | 0.20 | Exact | Axial | 2.275556e-5 | 22.755556 | 0.227556 |
| Example 2 | 0.20 | Dipole | Axial | 2.000000e-5 | 20.000000 | 0.200000 |
| Example 3 | 0.20 | Exact | Equatorial | 9.130352e-6 | 9.130352 | 0.091304 |
| Example 4 | 0.20 | Dipole | Equatorial | 1.000000e-5 | 10.000000 | 0.100000 |
Formula used
Definitions
m = dipole moment (A·m²)
L = magnetic length
a = half magnetic length = L / 2
p = pole strength = m / L
k = (μ0 μr / 4π) = 10-7 μr
Exact axial field
B = k · p · [1 / (x - a)2 - 1 / (x + a)2]
Exact equatorial field
B = k · m / (y2 + a2)3/2
Dipole axial approximation
B = k · (2m / x3)
Dipole equatorial approximation
B = k · (m / y3)
How to use this calculator
- Choose the calculation model. Use the exact model for closer points and the dipole model for far-field estimates.
- Select whether the point lies on the axial line or on the equatorial line of the bar magnet.
- Enter the dipole moment, magnetic length, and the distance from the magnet center.
- Pick the correct length units and set the relative permeability of the surrounding medium.
- Press the calculate button to show the field strength, gradient, comparison model, and graph above the form.
- Use the CSV and PDF buttons to export the current result summary and graph data.
FAQs
1) What is the difference between axial and equatorial field?
Axial field is measured along the magnet’s main axis. Equatorial field is measured on the perpendicular bisector through the center. Their magnitudes differ because geometry changes how each pole contributes to the final field at the observation point.
2) When should I use the exact model?
Use the exact finite magnet model when the observation point is not very far from the bar magnet. It accounts for the actual magnetic length and usually gives better results than the dipole approximation at short distances.
3) When is the dipole approximation acceptable?
The dipole approximation works best when the distance from the magnet is much larger than the magnetic length. In that region, the magnet behaves like an ideal dipole, making the simpler formulas practical and fast.
4) Why must exact axial distance exceed half the magnetic length?
The exact axial expression contains terms with x - a in the denominator. At or inside that location, the simple two-pole model becomes singular or nonphysical for this calculation setup, so the calculator blocks that input.
5) What does dipole moment mean here?
Dipole moment is a measure of magnetic strength and separation. In this calculator, it controls the overall field magnitude. Larger dipole moment values produce larger axial and equatorial magnetic fields at the same distance.
6) Why are Tesla, microtesla, and Gauss all shown?
Different textbooks, labs, and engineering references use different magnetic units. Tesla is the SI base unit, microtesla is convenient for smaller fields, and Gauss is common in older references and practical magnet discussions.
7) What is the field gradient used for?
The field gradient shows how quickly magnetic field changes with position. It is useful when estimating sensitivity, motion effects, magnetic force trends, and how strongly measurements may vary across a small distance range.
8) Does surrounding material affect the result?
Yes. Relative permeability scales the magnetic flux density in this model. Air and vacuum are close to 1, while some materials can raise the calculated B value. Always choose a realistic μr for your surrounding medium.