whats the mutual inductance?

Answer 1

When 2 inductors are placed so their magnetic fields coincide, a transformer is created.

Voltage (v2) in the 2nd inductor will be created by changing current (i1) in the 1st inductor by the formula:

v2 = M * d(i1)/dt

M is a constant of proportionality called the mutual inductance.

Another way to derive M, is by the formula:

M = k * sqrt(L1 * L2)

k is the coupling coefiicient (a number from 0 to 1)
L1 is the inductance of the 1st inductor
L2 is the inductance of the 2nd inductor
(sqrt is square-root)

k = magnetic flux common to both coils divided by the mag. flux in the 1st coil. If all the flux lines in the 1st coil are present to the second coil, k = 1. k is usually close to 1, like 0.98, or 0.95

k describes the efficiency of the transformer and takes leakage flux into account.
.

Answer 2

See http://library.thinkquest.org/16600/advanced/inductance.shtml