Two concentric circular coils one of small radius r1

Asked by admin @ 16/08/2021 in Physics viewed by 284 People

Consider two concentric circular coils,one of radius r1 and the other of larger radiusr2(r1＜＜r2),placed coaxially with centres coinciding with each other.obtain the expression for the mutual inductance of the arrangement.

Answered by admin @ 16/08/2021

N₁ = number of turns per unit length of inner coil
n₂ = number of turns per unit length of outer coil
r₁ = inner coil radius
r₂ = outer coil radius
μ₀ = permeability of free space
L = length of the coils (both)

Let i₁ be the current flowing in the inner coil.
Magnetic field B due to this current = μ₀ n₁ i
This field B is only inside the coil 1. Outside the coil 1, the field is 0.

Magnetic flux through 1 turn of coil 2 due to B is :
Φ = B * Area = μ₀ n₁ i * π r²

Total Number of turns in coil2 = n₂ * L
Total Magnetic flux through all the turns of coil 2
= Φ = μ₀ n₁ i * π r² * n₂ L

Mutual inductance M is defined as : Φ = M * i
So M = μ₀ n₁ n₂ π r² L

Mutual inductance per unit volume of the coils: μ₀ n₁ n₂

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Two concentric circular coils one of small radius r1

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