Define mutual inductance and write its S.I. unit

(a) Define mutual inductance and write its S.I. unit.
(b) Derive an expression for the mutual inductance of two long co-axial solenoids of same length wound one over the other.
© In an experiment, two coils ${ c }{ 1 }$
and ${ c }
{ 2 }$
are placed close to each other. Find out the expression for the emf induced the coil ${ c }{ 2 }$
due to a change in the current through the coil ${ c }
{ 2 }$.

(a) \phi =MI
Mutual inductance, between of two coils is equals to the magnetic flux linked with one coil when a unit current is passed in the other coil.
e=-M\frac { dI }{ dt }
Mutual inductance is equal to the induced emf set up in one coil when the rate of change of current flowing through the other coil is unity.
SI unit : henry, (weber { ampere }^{ -1 })
or (volt second { ampere }^{ -1 }). (Any one)