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egoodchild

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- TL;DR Summary
- Looking to learn how to calculate the distance from the center of a magnetic dipole to an arbitrary point in 3D space assuming we know the B-field at that arbitrary point as well as the characteristics of the dipole in question.

So I'm looking for some advice on a problem that I am trying to solve for a project. I'm an engineer but my background in vector mathematics is very minimal so I'm looking for some assistance.

Lets assume we have a permanent magnet. We know the characteristics of this magnet, such as it's dimensions and residual flux density, etc. Now let's say we pick some arbitrary point away from this magnet in 3D space and we define the distance from that point to the center of the magnet as 'r'. Additionally we measure the B-field at this arbitrary point and know the field strength in all 3 dimensions.

I would like to be able to calculate the distance 'r' from the center of magnet to the arbitrary point in meters.

Now from what I have gathered so far I think the way to do this is by using the equation for a magnetic dipole:

Above image from K&J Magnetics

Where m is:

B is known, m is known and we are looking to calculate 'r'.

Now where I get a bit lost is finding the reciprocal of this equation in vector form. As mentioned my end goal is an equation that has an input of B and output of r.

Any help on how to derive this or a resource to take a look at to help would be great.

Thanks in advance!

Lets assume we have a permanent magnet. We know the characteristics of this magnet, such as it's dimensions and residual flux density, etc. Now let's say we pick some arbitrary point away from this magnet in 3D space and we define the distance from that point to the center of the magnet as 'r'. Additionally we measure the B-field at this arbitrary point and know the field strength in all 3 dimensions.

I would like to be able to calculate the distance 'r' from the center of magnet to the arbitrary point in meters.

Now from what I have gathered so far I think the way to do this is by using the equation for a magnetic dipole:

Above image from K&J Magnetics

Where m is:

B is known, m is known and we are looking to calculate 'r'.

Now where I get a bit lost is finding the reciprocal of this equation in vector form. As mentioned my end goal is an equation that has an input of B and output of r.

Any help on how to derive this or a resource to take a look at to help would be great.

Thanks in advance!