Encyclopedia Magnetica™

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Magnetic field strength H of a cuboid (rectangular) permanent magnet along its axis
$$ H(x) = \frac{B_r}{π·µ_0}· \left( \text{atan} \frac{2·(x+L)·\sqrt{a^2+b^2+4·(x+L)^2}}{a·b} - \text{atan} \frac{2·x·\sqrt{a^2+b^2+4·x^2}}{a·b} \right) $$	(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)

Magnetic field along the axis of a cuboid magnet

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.