Encyclopedia Magnetica™

Stan Zurek, Calculator of H along axis of cylindrical magnet, Encyclopedia Magnetica,
http://e-magnetica.pl/doku.php/calculator/magnet_cylindrical, {accessed: 2025-04-27}

Magnetic field strength H of a cylindrical permanent magnet along its axis
Source: [1] Edward P. Furlani, Permanent magnet and electromechanical devices, Academic Press, London, 2021, ISBN 0122699513
[1], eq. (3.98), p. 129	(based on magnet diameter D)	$$ H(x) = \frac{B_r}{2·µ_0}· \left( \frac{x+L}{\sqrt{D^2 /4 +(x+L)^2}} - \frac{x}{\sqrt{D^2 /4 +x^2}} \right)$$	(A/m)
[1], eq. (3.98), p. 129	(based on magnet radius R)	$$ H(x) = \frac{B_r}{2·µ_0}· \left( \frac{x+L}{\sqrt{R^2+(x+L)^2}} - \frac{x}{\sqrt{R^2+x^2}} \right) $$	(A/m)
where: $B_r$ - remanence (flux density) of the permanent magnet (T), $L$ - axial length (m) of the cylindrical magnet, $D$ - diameter (m) of the of the magnet, $R$ - radius (m) of the of the magnet, $x$ - location (m) from the surface of the magnet (surface is synonymous with x = 0), μ₀ - magnetic permeability of vacuum (H/m)