Define ‘mutual inductance’ of to coil. On what factors it depends? Two concentric circular coils, one of small radius r 1 and the other of large radius r 2 , such that r 1

Question

Define ‘mutual inductance’ of to coil. On what factors it depends? Two concentric circular coils, one of small radius r 1 and the other of large radius r 2 , such that r 1 << r 2 , are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangement.

Philoid · Accepted Answer

Mutual induction is the process of induction of voltage in one coil due to the change in current of another coil close to it.

It is measured by the mutual inductance of the coil, L, given by the relation: ɸ₁ = Li₂... (i) where ɸ₁ = flux through first coil, i₂ = current flowing through second coil.

Diagram of problem:

Let the two loops carry currents i₁(r₁) and i₂(r₂) respectively.

Magnetic field induced at the centre due to the bigger loop(B),

Where μ₀ = magnetic permeability

Flux induced through the first coil = B x area of first coil,

= Li₂, according to (i).

Therefore, L is given by

Define ‘mutual inductance’ of to coil. On what factors it depends? Two concentric circular coils, one of small radius r1 and the other of large radius r2, such that r1 << r2, are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangement.

Define ‘mutual inductance’ of to coil. On what factors it depends? Two concentric circular coils, one of small radius r₁ and the other of large radius r₂, such that r₁ << r₂, are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangement.