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Magnetic Field of a Hollow Cylindrical Magnet

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This Demonstration shows the magnetic induction for a homogeneously axially magnetized hollow cylindrical magnet.

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is the length; , are the inner and outer radii of a magnet, respectively.

The magnetization A/m (remanent field ).

Consider the hollow cylindrical magnet as two cylindrical magnets with radii and , of equal length and magnetization. The magnetization directions of the cylinders are opposite. Therefore the magnetic field induction is calculated as the total of two cylindrical magnetic inductions .

Figure shows the component of total magnetic induction along the axis.

Figure shows dependence of the component of total magnetic induction on at .

Field lines of a hollow cylindrical permanent magnet involve the calculation of a large number of integrals. To improve accuracy, increase the number of points in the integrations or the number of points in the field-line plots. This will, however, increase the time required for computation.

You can change the sizes of the permanent magnet, but it it will take some time for the new calculations to run.

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Contributed by: Volodymyr Holovatsky and Yana Holovatska (Chernivtsi National University and Chernivtsi Liceum #1, Ukraine) (January 2020)
Open content licensed under CC BY-NC-SA

Details

References

[1] N. Derby and S. Olbert, "Cylindrical Magnets and Ideal Solenoids," American Journal of Physics, 78(3), 2010 pp. 229–235. doi:10.1119/1.3256157.

[2] Q. L. Peng, S. M. McMurry and J. M. D. Coey, "Axial Magnetic Field Produced by Axially and Radially Magnetized Permanent Rings," Journal of Magnetism and Magnetic Materials, 268(1–2), 2004 pp. 165–169. doi:10.1016/S0304-8853(03)00494-3.

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Volodymyr Holovatsky and Yana Holovatska (Chernivtsi National University and Chernivtsi Liceum #1, Ukraine) "Magnetic Field of a Hollow Cylindrical Magnet"
http://demonstrations.wolfram.com/MagneticFieldOfAHollowCylindricalMagnet/
Wolfram Demonstrations Project
Published: January 29 2020

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