# Electromagnetism issues need clearing up

## Main Question or Discussion Point

In electromagnetism, when there is an emf is induced in a secondary coil from a current flowing in a nearby primary coil (such as in a transformer), then how is the mutual inductance, number of turns of each coil, the current in the primary coil, and the emf in the secondary coil related?

From the reading that I have been doing, I think that for a single coil:
$$B = \frac{u_0NI}{2 \pi r}$$
Where the $u_0$ is the permeability of free space (I don't know how to get the proper symbol), $N$ is the number of turns, and $B$ is the magnetic field strength.

From what I have gathered from the reading, is:
$$E = -\frac{d \psi}{dt} = -L \frac{dI}{dt}$$
Where I have used $E$ for emf, and psi for the flux (I don't know how to get the convention symbol), and $L$ is the inductance of the secondary coil, however, I am unsure as to how the mutual inductance (M) is related to the inductance (L).

I think the problem is that when people speak of inductance, I am unsure what they mean the inductance of.

The reason why I am asking is that I have a question which uses this idea, but I am so close to getting it, that I would rather not post the problem in the homework section.

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## Answers and Replies

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Andrew Mason
Homework Helper
In electromagnetism, when there is an emf is induced in a secondary coil from a current flowing in a nearby primary coil (such as in a transformer), then how is the mutual inductance, number of turns of each coil, the current in the primary coil, and the emf in the secondary coil related?

From the reading that I have been doing, I think that for a single coil:
$$B = \frac{u_0NI}{2 \pi r}$$
Where the $u_0$ is the permeability of free space (I don't know how to get the proper symbol), $N$ is the number of turns, and $B$ is the magnetic field strength.

From what I have gathered from the reading, is:
$$E = -\frac{d \psi}{dt} = -L \frac{dI}{dt}$$
Where I have used $E$ for emf, and psi for the flux (I don't know how to get the convention symbol), and $L$ is the inductance of the secondary coil, however, I am unsure as to how the mutual inductance (M) is related to the inductance (L).

I think the problem is that when people speak of inductance, I am unsure what they mean the inductance of.

The reason why I am asking is that I have a question which uses this idea, but I am so close to getting it, that I would rather not post the problem in the homework section.
L, self inductance, is the ratio of induced emf in an inductor (coil) to rate of change of current in that inductor: Emf = L dI/dt

Mutual inductance relates to two coils in which a change of current in one coil induces an emf in the other. Emf = MdI/dt where Emf is the emf in the other coil.

AM

$\phi$?