=== Calculator of H along axis of rectangular magnet === |< 100% 10% 90% >| | {{/calculator/icon_calc.png?60&nolink}} | //[[user/Stan Zurek]], Calculator of H along axis of rectangular magnet, Encyclopedia Magnetica//, \\ @PAGEL@, {accessed: @YEAR@-@MONTH@-@DAY@} | ^ [[/Magnetic field strength]] //H// of a cuboid (rectangular) [[/permanent magnet]] along its axis ^^ | //Source [1] [[https://isbnsearch.org/isbn/0122699513|Edward P. Furlani, Permanent magnet and electromechanical devices, Academic Press, London, 2021, ISBN 0122699513]]// || | //[1], eq. (3.114), p. 135 (converted by [[/user/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), //μ//0 - [[/magnetic permeability of vacuum]] (H/m) || Magnetic field along the axis of a cuboid [[/magnet]] [[file/rectangular_magnet_field_magnetica_png|{{/rectangular_magnet_field_magnetica.png}}]] {{page>insert/by_SZ}}
Remanence Br = (T)     

Side a =     

Side b =

Length L =     

Position on axis x =



H =      B(μ0) =

//Notes: This is valid only for a uniformly magnetised cuboid magnet, for the field along its axis.[(Furlani>[[https://isbnsearch.org/isbn/0122699513|Edward P. Furlani, Permanent magnet and electromechanical devices, Academic Press, London, 2021, ISBN 0122699513]])] The value of B(μ0) is for vacuum. // ↑ {{page>insert/paypal}} {{tag>Magnetic_field_of_magnets Art Calculators}}