Encyclopedia Magnetica™

Calculator of H along axis of cylindrical magnet

This section is an interactive calculator.

Magnetic field strength H of a cylindrical permanent magnet along its axis
(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)
(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)

Magnetic field along the axis of a cylindrical magnet

^{S. Zurek, E-Magnetica.pl, CC-BY-4.0}

Notes: This equation is valid only for a uniformly magnetised cylindrical magnet, for the field along its axis.¹⁾ The value of B(μ₀) is for vacuum. More details are on the summary page https://e-magnetica.pl/art.

Calculators

¹⁾ Edward P. Furlani, Permanent magnet and electromechanical devices, Academic Press, London, 2021, ISBN 0122699513