Answer :

a) Mutual inductance is the property of two coils by the virtue of which each opposes any change in the value of current flowing through the other by developing an induced emf. The SI unit of mutual inductance is henry and

its symbol is H.

(b) Consider two long solenoids S_{1} and S_{2} of same length l such that solenoid S_{2} surrounds solenoid S_{1} completely.

Let:

=number of turns per unit length of

=number of turns per unit length of

= Current passed through solenoid

Where,

When current is passed through solenoid, an emf is induced in solenoid .

Magnetic field linked with each turn of solenoid on passing current through it is given by:

Magnetic flux linked with each turn of solenoid will be equal to times the area of cross-section of solenoid .

Magnetic flux linked with each turn of solenoid . Therefore, total magnetic flux linked with the solenoid is given by:

Where, is the total number of turns wound over the secondary coil.

Similarly the mutual inductance between the two solenoids when current is passed through solenoid and induced emf is produced in solenoid is is given by:

Where, N_{1}is the total number of wounds over primary coil.

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