Question

Figure shows two long coaxial solenoids, each of length ‘L’. The outer solenoid has an area of cross-section A₁ and number of turns/length n₁ The corresponding values for the inner solenoid are A₂ and n₂ Write the expression for self-inductance L₁, L₂ of the two coils and their mutual inductance M. Hence show that M <√L₂L₂.

Answer 1

Self-inductance of a solenoid of length L =µ₀n²AL, where n is number of turns per metre.

L₁ = µ₀n²₁A₁L

and L₂ = µ₀n²₂A₂L

If I₁ is the current in outer solenoid, then magnetic field at axis, B₁ = µ₀n₁I₁

Magnetic flux linked with the secondary coil