# Mutual inductance interpretation

How to explain mutual inductance with the image I attached? There are two conducting frames, one has a source of DC and a variable resistor, the other just a galvanometer. What I should conclude from this picture that the flux is F1=alpha*I and F2=c*F1, and Ein=-M*dI/dt. How? Is the current I, the induced current in the left frame or the changeable current in the right frame? Is F1 the flux for the left or the right frame?

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sophiecentaur
Gold Member
You may find it useful to look at Transformer Theory (which your experiment is an example of - even if it is a lousy example of a transformer!)

I don't want to get delve too deep into the unknown. I just want a rationalization of the experiment I posted.

anorlunda
Staff Emeritus
I can't find the one I need.

sophiecentaur
Gold Member
Mutual Inductance is a defined quantity and it tells you the induced emf in one coil, caused by the rate of change of current in the other. This is along the same lines as self inductance. So E = M dI/dt. Why or how it works is not considered in that definition. It's a quantity that can be used on its own as long as the elements are linear. (i.e. no saturating c

sophiecentaur
Gold Member
@Chemist@
You may be trying to second guess this thing. There will be an induced emf which could cause a current to flow (if the circuit is not open circuited) this current will affect the current that flows in the first (primary) coil because of the emf caused by the secondary current. etc. etc. . . . So it's all jumbled up and when you are using AC, can be described in an Impedance Matrix - shown in this link . If. the impedances are only Inductive then you will have a Reactance matrix of the same form.
You say this:
I don't want to get delve too deep into the unknown
but you can't really avoid getting in a bit deep, I'm afraid. The relationships described in this are what applies after a finite settling time - just as the currents in a resistive network. Components appear to 'know' about the presence of the other components because they all contribute to the final answer.

The electricity dI/dt in the formula is the electricity of the primary coil?

sophiecentaur
Gold Member
The Mutual Inductance is what causes a Voltage in one coil from the dI/dt in the other. But that doesn't happen in isolation, usually, which is why the volts and current in and out are related by that (matrix) Z parameter formula. Your questions seem to imply that you expect a simple answer and I don't think there is one. Look on that Wiki page at the Two Port network section, which says it all (sorry about the jargon but you can't avoid it.

I just need to know which current is used in the formula.

sophiecentaur
Gold Member
Post 9 tells you, I think.

So it is the current of the primary coil. The flux through it is c*I, and the flux through the second coil is alpha*c*I?

sophiecentaur
Gold Member
Mututal inductance is just the overall behaviour of the coils. There are many different designs for a pair of coils that will have the same Mutual Inductance and the Flux is a separate issue. Are you asking the right question for your needs?

I just need to derive the induced EMF. Is my reasoning correct?

sophiecentaur
Gold Member
If you know the M then you would know the emf in the other coil.
E2 = M12dI1/dt (The M suffix may be the wrong way round but no matter)
But what has that to do with Flux? Using M misses out the magnetic flux - same as the self Inductance value.
As I commented earlier, I don't think you are asking the right question because I have given you the answer to what M stands for. Could you expand on those initial formulae you are using and say where they come from? How "deep" are you prepared to go?

M=c*alpha and Ein=-dF/dt, and F=M*I. Now could I get a response to my previous posts.

sophiecentaur
Gold Member
M=c*alpha and Ein=-dF/dt, and F=M*I. Now could I get a response to my previous posts.
What is alpha? what is c? (speed of light?)?, what is F (Force?)? Or what reference do you have where those symbols are used - second thoughts, I would rather you told me because I am getting fatigued. I am not a mind reader.

Edit - sorry, I can see some of what you mean (caught me at a bad moment and I don't know how to strike through text) but I am not familiar with where you are going. M is defined (already). How are the DC conditions relevant to M? Can you show some workings - from a reference? It means nothing to me, so far. I'm not even sure of the context.

Have you tried a conventional (text book) approach to get what you want?

Last edited:
c and alpha are proportionality constants. Here is what I got: DC passes through the right coil, but it changes over time because of the variable resistance so it produces a magnetic field with a flux through the left frame of F=c*I, and through the second: F=c*alpha*I=MI. The induced EMF in the right coil is EMF=-dF/dt=-M*dI/dt, that's the full story as I understand it. Is my reasoning correct?

sophiecentaur