Calculator of H along axis of rectangular magnet
 | Stan Zurek, Calculator of H along axis of rectangular magnet, Encyclopedia Magnetica, http://e-magnetica.pl/doku.php/calculator/magnet_rectangular, {accessed: 2025-03-14} |
| Magnetic field strength H of a cuboid (rectangular) permanent magnet along its axis | |
|---|---|
| Source [1] Edward P. Furlani, Permanent magnet and electromechanical devices, Academic Press, London, 2021, ISBN 0122699513 | |
| [1], eq. (3.114), p. 135 (converted by Stan Zurek to be expressed by remanence flux density rather than saturation magnetisation | |
| $$ H(x) = \frac{B_r}{π·µ_0}· \left( \text{atan} \frac{2·(x+L)·\sqrt{a^2+b^2+4·(x+L)^2}}{a·b} - \text{atan} \frac{2·x·\sqrt{a^2+b^2+4·x^2}}{a·b} \right) $$ | (A/m) |
| where: $B_r$ - remanence (flux density) of the permanent magnet (T), $L$ - axial length of the cuboid magnet (m), $a$ and $b$ - lengths (m) of the sides of the cuboid magnet, $x$ - location (m) from the surface of the magnet (surface is synonymous with x = 0), μ0 - magnetic permeability of vacuum (H/m) | |
Notes: This is valid only for a uniformly magnetised cuboid magnet, for the field along its axis.1) The value of B(μ0) is for vacuum.
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