# Mutual Inductance Calculation

#### HiEdgar

Hi, All:

I am trying to calculate the mutual inductance between the coil (100 turns) and the magnet. Does anybody know any approaches that may lead a satisfactory answer.

So far, I have been using Neumann's formula which is the formula for mutual inductance, M, between two loops. I treated my magnet as another coil and used Neumann's formula to determine M then. The problem with that is that the diameter of the wires of my coil are finite whereas neumann's formula treats them as infinitisemally small. Because of this, my M became a funciton of magnet's wire diameter, which is not right. Any input is appreciated.

Thank you,

Edgar

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#### zoobyshoe

As far as I know "mutual inductance" is the term used to describe what happens in a transformer, and is synonymous with "mutual induction". That being the case I'm confused by your question, because you speak only of one coil and refer to a magnet. In a transformer there should be at least two coils and a core, but no magnet.

It could be that "mutual inductance" was used by mistake in the old book I looked it up in but I'n not sure. Another book I have used the term "mutual induction" to describe the same thing.

Zooby

#### HiEdgar

Hi,

I am not working with transformers. My objective is to measure the strength (Br) of a given magnet. The experimental setup is as follows: as we move the magnet closer to the coil, there will be emf generated in teh coil. In can be shown that the strength of a magnet is proportional to the
Integral[emf]/delta_[M], where M is the mutual inductance. I can measure Integral[emf]. But I need to know M, which is a function of a position. My first approach was to use Neumann's formula which you can find in Griffiths' or Jackson's E&M textbooks. However Neumann's formula deals with wires whose diameter is infinitesimally small.

From your email, I also got a feeling that you may know some techniques on calculating the emf induced in the coil due to magnet's movement. Formulawise, it is not bad: emf=-N dFlux/dt, Flux=Integral{B.da}, B=mu0 H, H=-Grad[Phi_m], Phi_m=Integral[n.M/r da]. Unfortunately, when I used this approach, the math got so hairy after calculation of B that is was really hard to go further. If you know of any other approaches please let me know,

thank you,

Edgar

#### zoobyshoe

Sorry to say, now that I understand the situation you're trying to work with, that I don't know what you need to work the problem out. It sounds to me like the kind of problem that would arise in the engineering of generators. If you can find any literature on that it may help.
"From your email, I also got a feeling that you may know some techniques on calculating the emf induced in the coil..."
I didn't send you an E-Mail, so this statement is unsettling. You recieved an E-Mail from me? zoobyshoe?

#### dudelalit

i need the neumanns eqn derivation part as well as how it can be applied to calculate mutual inductance?????

#### sophiecentaur

Gold Member
Where does your "mutual inductance" come into it?
Mutual inductance tells you the emf generated in one winding when the current in another winding changes. Where are the 'two' windings in this model?

#### Mike_In_Plano

Attempting to measure theintegral of the induced EMF could get pretty hairy since measurement errors could quickly overwhelm out your data (unless you made the measurement quickly.

In the lab, we would typically use a Bell gaussmeter. If your low on resources, perhaps measuring the force on a current bearing coil (Lozentz force) could help you out. That or purchasing a cheap Hall sensor, then zeroing and scaling it with a homemade helmholtz coil.

Best of luck,

Mike

#### dudelalit

yeah yeah i got it :)
thank u

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