What is the formula for magnetic force produced by a permanent magnet?
Dear Nicolette,
If you want to know the force on an electric charge then you must apply the Lorentz formula.
Perhaps it would be good that you look for this issue in the reference:
Griffiths, David J. (1998). Introduction to Electrodynamics (3ª ed.). Prentice Hall
It depends on the magnetic field generated by a permanent magnet:
In uniform magnetic field the force acting on magnetic moment m is zero. However there is non-zero torque t: t=mxB (in vector notation).
In non-uniform magnetic field the force acting on magnetic moment is: F=(m•nabla)B
see also: https://en.wikipedia.org/wiki/Magnetic_moment
Dear Nicolette,
Bartlomiej is answering the inverse question to the one, you are asking. The force produced by the magnet depends on the its shape, material etc. and on the other hand on the position of the object (characterized by its magnetic moment) in the non-uniform magnetic field produced by the magnet.
In this sense the Batlomiej answer "the force acting on magnetic moment is: F=(m•nabla)B " is true and exact, but your general question has no answer without specifying number of specific conditions and circumstances.
Let us to be a little bit more explicit. The permanent magnet is a source of magnetic field H and induction B which are non uniformly distributed in space. If a charge body approach its motion depends of the relative velocity v, the electric charge q and the magnetic induction following Lorentz formula
F= q v x B
where you can see that the velocity v is always orthogonal to B and therefore there is no exchange of energy.
The permanent magnet can also interact with other magnet. For calculating the interaction of these two magnets it is convenient to consider two ideal cases:
1. each magnet is formed by two poles (north and south) that can be interacting independently if the magnets are long enough
F= μ g1 g2 / 4ᴫ r2
Where g1 and g2 are magnetic poles in ampere-meter, μ is the magnetic permeability of the medium in tesla-meter per ampere and r the distance between the poles. N-n and s-s repelrepel while n-s or s-n attract.
2. if the mangnets are short enough and its poles are closer each other,, then you can consider it a magnetic dipole and two magnets will interact as
F= 3 μ0/4 ᴫ r5 [((r x m1) x m2 + (r x m2) x m1 -2 r (m1.m2)) + 5 r (r x m1).(r x m2)/ r3]
Given that the magnetic fields distribute quite non uniformly in space and which depends non linearly of the direction between the dipoles, it is very difficult to generalize the formulae and the best is to go to one text as the one that I have recommended you.
Better if I introduce a parenthesis more for distinguishing the first product
F= (3 μ0/4 ᴫ r5) [((r x m1) x m2 + (r x m2) x m1 -2 r (m1.m2)) + 5 r (r x m1).(r x m2)/ r3]
Daniel Baldomir I want to calculate the magnetic force in axial and radial directions of two concentric ring magnets with (i) axial magnetization and (ii) with skewed magnetization i.e. when magnetization is not perfectly axial but could be skewed by say 2-3degrees. I am a mechanical engineer so a bit out of my comfort zone here. I have seen Yonnet's papers on magnet bearings. But would you be able to provide/suggest some more introductory material through which I can understand the basics of permanent magnets, their material properties and the field they generate before I attempt solving the complex formulae in Yonnet's paper. Any help would be gratefully received. Thanks.
Dear Gan Jia Gui
You should clarify more about your question. I saw your page and realized that you must have asked about magnetic body force in fluid mechanics domain. Please take a look at following papers. It will be helpful.
1. Heat transfer enhancement of a fin-and-tube compact heat exchanger by employing magnetite ferrofluid flow and an external magnetic field ,
- 10.1016/j.applthermaleng.2019.114462
2. Effect of magnetic field on the hydrodynamic and heat transfer of magnetite ferrofluid flow in a porous fin heat sink ,
- 10.1016/j.jmmm.2019.01.028
is it possible to find the magnetic force due to a magnet on a steel ball kept at a distance r from it
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