# Mutual Induction-Definition, Example, And Formula

The phenomenon in which a changing **current** in one coil **induces an emf** in another coil is called Mutual induction.

**Mutual induction**

It is the opposite of **self-induction**. In self-induction, emf produce in the same coil but in mutual induction, the fields of one coil induce an emf in another coil. For Example, The basic working principle of a **transformer** is mutual induction.

**Mutual induction Formula**

Consider two coils placed closed to each other. The coil connected with a battery through a switch and a rheostat is called the “Primary” and the other one connected to the **galvanometer** is called the Secondary coil.

If the current in the primary is changed by the rheostat, the magnetic flux in the surrounding region changes. Since the changing **flux** is also linked with the secondary, it causes an induced emf in the secondary. According to Faraday’s law

ԑ_{s}=N_{s }Δ ϕ_{s}/ Δt

Where

ԑ_{s} =induced emf in the secondary.

ԑ_{s}= number of turns in secondary

Δ ϕ_{s}/ Δt =rate of change of flux in secondary,

If the flux passing through one loop of the secondary coil is ϕ_{s }then the net flux passing through the coil of Ns’ loops Ns ϕ_{s},

As the magnetic flux through the secondary coils is proportional to the current in the primary coil, then

N_{s} ϕ_{s} ∝ l_{p}

N_{s} ϕ_{s}=Ml_{p}

Where M is the constant of proportionality called the Mutual Inductance.

ԑ_{s} =-N_{s}(Δ ϕ_{s}/ Δt)

ԑ_{s} =- Δ ( Ml_{p} / Δt)

ԑ_{s }=-M (Vl_{p }/ Δt)

M=ԑ_{s}/ Vl_{p }/ Δt)

The induced emf in the secondary is proportional to the time rate of change of current in the primary.

**Mutual inductance:**

The ratio of average emf induced in the secondary coil to the change of current with time in the primary coil.

**Unit of mutual induction:**

The SI unit for the mutual inductance M is VsA^{-1}, which is called a henry (H).

**What is Henry?**

One henry is the mutual inductance of the pair of coils in which a rate of change of current of one ampere per second in the primary causes an induced emf of one volt in the secondary.

**Factors affecting the Mutual Inductance**

Factors upon which mutual inductance depends

- Mutual inductance depends upon
- Number of turns of the two coils
- The cross-sectional area of the coils
- The closeness of the coils
- Nature of the core material upon which coils are wound

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