Question

Define the coefficient of mutual inductance. Give its unit and dimensional formula.

Answer 1

Coefficient of Mutual Inductance:

If orientation, size and shape of primary coil C₁ and secondary coil C₂, remains same and in coil C₁ current is I₁, then second coil C₂ is related to magnetic-flux which is proportional to the flow of current I₂. i.e.,
ϕ₂ ∝ I₁
or ϕ₂ = MI₁ ………… (1)
Here, M is proportionality constant, which is called mutual induction. Its value depend upon number of turns, area of secondary coil and medium.
If the current in coil C₁ changes with time, then flux linked with C₂, i.e.,ϕ₂ changes. Thus, induced emf in coil C₂,

The negative sign in equation (2), indicate that the direction of induced emf in secondary coil opposes the growth or decay of current flow in a primary coil, from equation (1),
ϕ₂ = MI₁
If I₁ = 1 Amp
then M = ϕ₂ ………………… (2)
Thus the coefficient of mutual inductance is equal to the magnetic flux linked with secondary coil when the current flow in a primary coil is unity, from equation (2),

then M = ε₂
Hence the coefficient of mutual inductance is equal to the induced emf when decay rate of current in primary coil is unity.
The unit of mutual inductance
M = \(\frac{Weber}{Amp}\) or henry (H)

Mutual inductance depends upon the number of turns in a coil, area of cross section and medium.

The S.I. unit of M is Wb/A or VA/A or henry (H) and its dimensions are [M¹L²T^-2A^-2].