Magnetic field of cylindrical magnet

[sgsawant]

Hi,

I wanted to calculate the magnetic field of a cylindrical magnet at a point P (r,ɵ,z). The magnet can be at the origin or anywhere convenient. Preferably the axis of the magnet is aligned with the z axis.

The magnet is of radius r_m and height h_m. The remanent flux density of the magnet is B_r. I have seen a few papers, but some of them are too complex. The simple solutions too, involve models which have unclear assumptions.

If you know a good analytical model, please point me in the right direction. I know that using FEM (say COMSOL) it is really easy.

Regards,

-sgsawant

 

[chrisbaird]

http://faculty.uml.edu/cbaird/all_homework_solutions/Jackson_5_19.pdf"

 

[sgsawant]

Thanks! But that's a very specific case - I am necessarily looking for a general case solution.

I appreciate your effort though.

 

[Enthalpy]

It's just that there is no simple solution, analytical and general.

As you may often expect when a field defined by a differential equation has edgy boundaries.

And as you may expect about every time with the magnetic field, because it makes no huge difference between conductors and isolators.

 

[sardar]

Hello sgsawant,

Thank you for your question about calculating the magnetic field of a cylindrical magnet. This is a common problem in magnetostatics and there are several analytical models that can be used to calculate the magnetic field at a specific point. One commonly used model is the Biot-Savart law, which describes the magnetic field produced by a current-carrying wire. In this case, the cylindrical magnet can be approximated as a series of small current loops along its surface, and the magnetic field at a point can be calculated by summing the contributions from each loop. This approach can be used for both axis-aligned and non-axis-aligned magnets.

Another useful model is the Ampere's law, which relates the magnetic field to the current enclosed by a closed loop. This can be applied to a cylindrical magnet by considering the magnet as a series of current-carrying rings stacked on top of each other. The magnetic field can then be calculated using the current enclosed by the rings.

If you are looking for a more simplified solution, you can also use the dipole approximation, which assumes that the magnetic field of the cylindrical magnet can be approximated as that of a point dipole located at the center of the magnet. This approach is useful for quickly estimating the magnetic field at points close to the magnet, but may not be accurate for points further away.

I recommend consulting with a textbook or online resources for more detailed explanations and derivations of these models. Additionally, as you mentioned, using finite element methods (FEM) with software such as COMSOL can provide accurate and efficient solutions for more complex magnet geometries. I hope this helps guide you in the right direction. Good luck with your calculations!

Best regards,