The phenomenon in which a changing current in one coil produces an induced emf in another coil is called mutual induction.
The coil is connected to a battery through a switch and a rheostat is called the primary coil.
When the primary and the secondary coil are placed face to face and the current in the primary is changed by varying the resistance of the rheostat, the magnetic flux in the surrounding region changes. This changing flux also changes the flux of induced emf in the secondary coil.
Expression for Mutual Inductance
let the flux pass through one loop of the secondary coil. The net flux passing through the coil of the Ns loop will be Ns. This flux is proportional to the magnetic field produced by the current Ip in the primary and the magnetic field itself is proportional to Ip, then
Ns ∅s ∝Ip
Ns ∅s = M Ip → eq1
Where M = (Ns ∅s)/Ip is the constant of
Proportionality is called the mutual inductance of the two coils.
Mutual inductance depends upon:
(i) The number of turns of the coil.
(ii) Cross-sectional area of the coil.
(iii) Closeness of the coil.
(iv) The number of the cores material.
(v) Rate of change of current in the primary coil.
According to Faraday’s law, the induced emf in the secondary coil is given the rate of change of flux through the secondary coil.
εs = – Ns (∆∅s)/∆t =- ∆(Ns∅s)/∆t→ eq2
from eq1 Ns ∅s = MIp
putting in eq2
εs = – (∆(MIp))/∆t = – M ∆Ip/∆t
εs = – ∆Ip/∆t → eq3
This shows that the emf induced in the secondary coil is proportional to the time rate of change of current in the primary coil and the +ve sign shows that the induced emf opposes the change of the primary the primary coil.
from eq 3,
M = -εs/(∆Ip⁄∆t) → eq4
The ratio of induced emf in the secondary coil to the rate of change of current in the primary coil is called mutual inductance.
M= εs/(∆Ip⁄∆t) = v/(a\/s)
M = VSA¯¹ = Henry
Mutal inductance of two coils is one hand if current changes at the rate of one ampere per second in the primary coil causing an induced emf of one volt in the secondary coil.