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# Difference between mutual and self induction

## What is Mutual induction?

“The process of inducing e.m.f in the secondary coil by changing the magnetic flux of the primary coil with the help of varying current through it is called mutual induction.”

If two coils placed together ,then by changing current in one coil sets up a changing magnetic field in the other coil,so induced an e.m.f in the other coil.

mutual induction

Consider two coils located near each other.The coil with the battery circuit is called the primary coil and the coil joined with galvanometer circuit is called the secondary coil.The secondary coil within the magnetic field of current carrying primary coil.The current in primary coil can changed by rheostat.

If current is changed in primary coil ,the magnetic flux through the secondary coil due to primary also changes.So,an emf will induced in the secondary coil also.

### Derivation of mutual induction:

$\{E s }\propto \frac { { \triangle I }_{ P } }{ \triangle t } \\ { E }_{ s }=-M\frac { { \triangle I }_{ P } }{ \triangle t } ——-(1)\\ Where\quad M\quad is\quad the\quad constant\quad of\quad proportionality\quad called\quad mutual\quad induction\quad and\quad negative\quad sign\quad is\quad due\quad to\quad lenz’s\quad law.\\ According\quad to\quad faraday’s\quad law\quad of\quad electroma$

Where M is the constant called a mutual induction and negative sign is due to lenz’s law.

According to Faraday’s  law of electromagnetic induction:

$\\\ { E }_{ s }=\frac { -N\triangle \Phi }{ \triangle t } ——-(2)\\ By\quad equating\quad equation\quad (1)\quad and\quad (2),we\quad get\\ \frac { -M\triangle { I }_{ P } }{ \triangle t } =\frac { -N\triangle \Phi }{ \triangle t } \\ M\triangle { I }_{ P }=N\triangle \Phi \\$

The S.I unit of mutual induction is Henry.

## Self induction:

“The process of inducing emf in the coil due to change of current in coil itself is called self induction.”

The change in the magnetic flux in a coil may be due to the relative motion of the coil and the magnetic field or due to the change of current in the coil itself.

Let us consider a coil of n turns with a battery,a galvanometer and a rheostat in its circuit.If current in the coil is changed with the help of rheostat,then change of magnetic flux also be felt in the coil itself,therefore inducing an e.m.f in coil is:

According to faraday’s law of electromagnetic induction:

$\emf\propto -\frac { \triangle I }{ \triangle t } \\ emf\quad =-L\frac { \triangle I }{ \triangle t } \quad \quad ——–(1)\\$ $\\quad \quad emf\quad =-\frac { \triangle N\Phi }{ \triangle t } ——-(2)\\ By\quad equating\quad equation\quad (1)\quad and\quad (2\quad )\quad we\quad get\\ \frac { -L\triangle I }{ \triangle t } =\frac { -N\triangle \Phi }{ \triangle t } \\ \\ L\triangle I=N\triangle \Phi \\$

Where L is called self induction constant.The S.I unit of self induction is Henry.

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