Mutual inductance

Inductance

Inductance is the conductor’s property (typically in coil-form) that’s measured through emf (electromotive force), or the voltage produced in it compared to the proportional change of the current that generates the voltage. A constant current, alternating current, or fluctuating direct current produces a variable magnetic field, which induces an electromotive force in any conductor present in the field.

The induced electromotive force is proportional to the electric current rate of change. The inductance factor is defined as the magnitude of the rate of change of the current causing the induction divided by the amount of the electromotive force generated in a conductor.

Mutual induction occurs when the electromotive force is induced in a conductor that is not the same as the one in which the current is changing.

What is Mutual Inductance?

The primary functioning concept of generators, motors, and transformers is mutual inductance. The same principle applies to any electrical device containing components that interact with another magnetic field.

Mutual induction, in which current flowing in one coil generates a voltage in a secondary coil, is usually responsible for the interaction. When two wire coils are brought near enough together that the magnetic field from one collides with the magnetic field from the other, a voltage is formed in the second coil.

When a voltage is applied to one coil, it induces a voltage in another. This is known as mutual inductance. The unit for measuring mutual Inductance is Henry, and its symbol is H.

Understanding Mutual Inductance

• Take two coils, P and S (Distinct coils) and place them side by side.
• One coil is connected to a switch, while the other is connected to a galvanometer.
• When a variable current is generated in coil P, a current is induced in coil S automatically.
• The primary coil is the P coil, and the secondary coil is the S coil, in which we witness the deflection.
• The P coil generates variable magnetic field lines that run through both coils as its current varies.
• This indicates that the current is increased, which causes the magnetic field lines to expand, increasing the flux at the secondary coil.
• When the flux rises, the coil generates an induced EMF, which causes an induced current to flow. As a result, a deflection is seen on the galvanometer.
• We curl our right hand’s fingers around the wire to identify the direction of the magnetic field lines, the direction in which the thumb points is the magnetic field’s direction.
• The magnetic field lines can be seen to be parallel to the current direction.
• When the flux in the secondary coil changes as a result of the changing current, an induced emf and induced current are generated.

Mutual Inductance Formula

The formula of two coils is given as

M = μ0N1N2A/l

Where μ0= permeability of free space =

N1= turns of coil 1

N2= turns of coil 2

A= cross-sectional area in m2

L = length of the coil in metres.

The unit of mutual inductance is kg. m2.s-2.A-2

The amount of inductance produces the voltage of one volt due to the rate of change of current of 1 Ampere/second.

EMF of mutual inductance

The electromotive force induced in a coil by a flux change produced by another coil connected to it is known as mutually induced EMF. Let us look at an example to better comprehend the concepts of mutually induced emf.

Consider two coils, A and B.

Coil B has N2 turns and is placed next to coil A, which has N1 turns.

When the switch (S) in the circuit is closed, current I1 flows through coil A, producing the flux φ1. The majority of the flux indicates φ12 links with the other coil B.

When the current flowing through coil A is changed by changing the value of variable resistor R, the flux linked with the other coil B changes, and thus emf is induced in the coil.

This induced emf is called emf of mutual inductance.

The direction of the induced emf is such that it opposes the cause, that is, the change in current in the first coil.

This effect of opposition caused by its reason for production is Lenz’s Law.

A galvanometer (G) is connected to coil B to measure the induced emf.

Conclusion

The property of a coil resisting current change in the adjoining coil is called mutual inductance. When the current in a neighbouring coil changes, the flux in the coil changes, causing a changing flux called mutually induced emf.