Answer :

(a) Mutual inductance is the property of two coils that opposes the change in current in one coil.

There are two Coils: coil 1 and coil2 with the number of turns N_{1} and N_{2}. The magnetic flux across them is and respectively. Let the current through coil 1 be and current through coil 2 be . Then, the mutual-inductance is given by:

(b)

**Concepts/Formulas used:**

__Force between two wires:__

If two straight infinite parallel conducting wires with current and are separated by a distance , then force per unit length of each wire is given by:

where is the magnetic permeability of free space.

If the wires carry currents in the same direction, they attract and if they carry currents in opposite direction, they repel.

By symmetry, and must be equal. Hence, they cancel out.

Now,

Also,

The total force is

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