Calculating Magnetic field of permanent magnet

In summary, a magnetic field around a permanent magnet can be calculated using Maxwell's equations, but the field lines must be drawn accurately to avoid errors.
  • #1
Hobnob
22
0
Hi: I'm having real trouble finding resources for the problem of accurately calculating (and drawing the field lines for) a magnetic field around a permanent bar magnet, or between two permanent magnets (I assume this is the same problem, as fields are superposable). I've found lots of sites talking about Maxwell's equations, but nothing about how to relate this to permanent magnets, rather than fields induced by currents. For that matter, I'm a little lost even with Maxwell's equations, as my field calculus is *very* rusty and was never that good to start with... I can't quite see how to move between the path/surface integrals and the actual field at a particular point.

Can anyone point to some good resources for someone who needs a bit of hand-holding but is ultimately up to the task?

All this is ultimately to be part of a motor/generator simulator, so a final question is: can I manage by just pre-calculating the magnetic field and superposing it on the field from the wire, or am I barking up completely the wrong tree?

Thanks
 
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  • #2
in first approximation the field well outside the magnet is a usual dipole field.
The next step is quite troubling, because you need to take into the account the effect of one part magnet on the magnetization of another part of the magnet. The problem is that you may have hysteresis und saturation. I have now idea how take the hysterisis into the account, but saturation is fine, as soon as you are using a computer.
The problem may be formulated like this:
let's imagine we have a small dipole with a magnetic moment [tex]M[/tex]. Then, if we put another dipole near it, their magnetic field will be a superposition of two dipoles. But their dipole moments will be affected by the external magnetic field from another dipole. The additional induced magnetic moment will be proportional to the external magnetic field and the dipole's supsceptibility, which may be nonlinear function of the external magnetic field.
 
  • #3


I understand your frustration in finding resources for accurately calculating and drawing the magnetic field of a permanent magnet. This is a complex problem that requires a combination of mathematical understanding and knowledge of the physical properties of permanent magnets.

One approach to calculating the magnetic field of a permanent magnet is to use the Biot-Savart law, which relates the magnetic field at a point to the current flowing through a wire. In the case of a permanent magnet, the magnetic field is generated by the alignment of the magnetic domains within the material.

Another approach is to use the concept of magnetic dipole moment, which is a measure of the strength and direction of a magnet. This can be calculated using the properties of the magnet, such as its length, width, and strength. The magnetic field at a point can then be calculated using the dipole moment and the distance from the magnet.

There are also computer programs and simulations available that can help you visualize and calculate the magnetic field of a permanent magnet. These programs use mathematical models and algorithms to accurately simulate the behavior of the magnetic field.

In terms of your final question about pre-calculating the magnetic field and superposing it on the field from the wire, it is possible to do so but it may not provide an accurate representation of the actual magnetic field. This is because the magnetic field can change depending on the position and orientation of the permanent magnet.

I recommend consulting with a physics professor or expert in the field to guide you in your calculations and provide resources for further understanding. It is also important to have a strong understanding of Maxwell's equations and vector calculus in order to accurately calculate the magnetic field. With some guidance and practice, you should be able to accurately calculate and draw the magnetic field of a permanent magnet for your motor/generator simulator.
 

1. What is the formula for calculating the magnetic field of a permanent magnet?

The formula for calculating the magnetic field of a permanent magnet is B = μ0 * (m / (4πr^3)), where B is the magnetic field strength, μ0 is the permeability of free space, m is the magnetic moment of the magnet, and r is the distance from the magnet.

2. How do you determine the magnetic moment of a permanent magnet?

The magnetic moment of a permanent magnet can be determined by multiplying the strength of the magnet by its pole area. This can be measured using a magnetometer or by using the formula m = N * I * A, where N is the number of turns in the coil of the magnetometer, I is the current passing through the coil, and A is the cross-sectional area of the coil.

3. Can the magnetic field of a permanent magnet be changed?

No, the magnetic field of a permanent magnet cannot be changed. It is a characteristic of the material and shape of the magnet and remains constant as long as the magnet is not demagnetized.

4. How does the distance from a permanent magnet affect the strength of its magnetic field?

The strength of the magnetic field of a permanent magnet decreases as the distance from the magnet increases. This relationship follows an inverse square law, meaning that the magnetic field strength is inversely proportional to the square of the distance from the magnet.

5. Can the magnetic field of a permanent magnet be shielded or blocked?

Yes, the magnetic field of a permanent magnet can be shielded or blocked by using materials such as iron, steel, or other ferromagnetic materials. These materials redirect the magnetic field lines, effectively shielding the magnet's field from being detected or affecting other objects.

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