**NEET Physics Notes Electromagnetic Induction-Mutual induction**

**Mutual induction**

**Mutual Induction**

Mutual induction is the phenomenon due to which an emf is induced in a coil when the current flowing through a neighbouring coil changes.

**Mutual Inductance**

Mutual inductance of a pair of coils is defined as the magnetic flux linked with one coil when a constant current, of unit magnitude, flows through the other coil.

Mathematically,

where, M is known as the mutual inductance for the given pair of coils.

Induced emf due to mutual inductance

Hence, mutual inductance for a pair of coils is numerically equal to the magnitude of induced emf in one coil when current in the other coil changes at a rate of 1 As^{-1}.

SI unit of mutual inductance M, is henry.

Mutual inductance of a pair of coils is maximum, when the two coils are wound on the same frame. However, mutual inductance is negligible when the two coils are oriented mutually perpendicular to each other (figure). In this context we define a term coupling coefficient k.

**0 ≤ k ≤ 1**

**Formulae for Mutual Inductance**

- Assuming the coupling coefficient k = 1 and medium to be a free space or air.

Mutual inductance of a pair of concentric circular coils is

where, r = radius of the coil (of small radius) and R = radius of the coil (of larger radius). - For a pair of two solenoid coils, wound one over the other

- For a pair of concentric coplanar square coils

where, a = side of the smaller coil and b = side of the larger coil. - For a given pair of coils, mutually coupled, then according to theorem of reciprocity.

M_{12}= M_{21}= M

**Combination of Inductors**

- If two coils of self-inductances and L
_{2}are placed quite far apart and are arranged in series, then their equivalent inductance

**L**_{s}= L1 + L 2 - However, if the coils are placed quite close to each other so as to mutually affect each other, then

**L**_{s}= L_{1}+ L_{2}± 2M - Here, M has been written with ± sign depending on the fact whether currents in the two coils are flowing in same sense or opposite sense.
- If two coils of self-inductances L
_{1}and L_{2}are connected in parallel, then equivalent inductance L_{p }is given by

- In a parallel arrangement, effect of mutual inductance may be omitted, because value of k in this arrangement is quite small.

**Eddy Currents**

Currents induced in the body of bulk conductors are called the eddy currents.

The production of eddy currents in a metallic conductor leads to a loss of electric energy in the form of heat energy.

Eddy currents can be minimised by taking the metal (generally soft iron) core in the form of a combination of thin laminated sheets or by slotting process.