Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2 , the mutual inductance M between them will be directly proportional to :

Concept:

When two coils are brought near to each other, then the magnetic flux linked with one coil leads to generation of voltage in the second coil due to changes in its magnetic flux, this property is known as mutual induction.

Because of Mutual induction voltage (Current) of a coils changes due to magnetic field of another coil brought near to it.

Calculation:

Two concentric coils are of radius R1 and R2 as shown

Let current in outer loop be i

Magnetic field at centre, \( B= \frac{{\mu_0 i}}{{2{R_1}}}\)

Magnetic flux through inner coil \( = B \times \pi R_2^2\)

\(ϕ = \frac{{{\mu _0}i}}{{2{R_1}}} \times \pi R_2^2\)

\(ϕ = \frac{{{\mu _0}i}}{2} \times \frac{{\pi R_2^2}}{{{R_1}}}\)

as per definition, ϕ = Mi

\( \Rightarrow M = \left( {\frac{{{\mu _0}\pi }}{2}} \right)\frac{{R_2^2}}{{{R_1}}}\)

\(\therefore M \propto \frac{{R_2^2}}{{{R_1}}}\)