Define the term 'mutual inductance' between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length $l$ and radii $r_{1}$ and $r_{2} (r_{2} >> r_{1})$ . Total number of turns in the two solenoids are $N_{1}$ and $N_{2}$ respectively.

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Solution

A coil B kept near another coil A has magnetic flux passing through it when kept near coil A. The ratio of magnetic flux through the coil B to the current in the coil A is called as mutual inductance of coil A and coil B.
$M_{12} = \frac{ϕ_{2}}{i}$

Let $S_{1}$ carries a current $i$ .
Magnetic field inside $S_{1}$ will be $B = μ_{o} N_{1} i / l$

Flux through each turn of $S_{2}$ is $ϕ = B \times π r_{2}^{2}$
$ϕ = μ_{o} N_{1} π r_{2}^{2} i / l$
Flux through all turns of $S_{2}$ is $ϕ_{B} = ϕ N_{2}$
$ϕ_{B} = μ_{o} N_{1} π r_{2}^{2} i N_{2} / l$
$M = \frac{ϕ_{B}}{i} = \frac{μ_{o} N_{1} N_{2} π r_{2}^{2}}{l}$

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Define the term 'mutual inductance' between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r1 and r2(r2>>r1). Total number of turns in the two solenoids are N1 and N2 respectively.

Define the term 'mutual inductance' between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length $l$ and radii $r_{1}$ and $r_{2} (r_{2} >> r_{1})$ . Total number of turns in the two solenoids are $N_{1}$ and $N_{2}$ respectively.