A solenoid `S_1` is placed inside another solenoid `S_2` as shown in The radii of he inner and the outer solenoids are `r_1` and `r_2` respectively and the numbers of turns per unit length are `n_1` and `n_2` respectively. Consider a length I of each solenoid. Calculate the mutual inductance betwwen them.

Answer

A

Explanation

(1) Magnetic field due to outer solenoid
`B_(2)=mu_(0)n_(2)i`
Flux through solenoid (1) `phi=B_(2).(n)_(1)l)(pir_(1)^(2))=mu_(0)n_(2)ilpir_(1)^(2)=Mi`
`M=mu_(0)pin_(1)n_(2)r_(1)^(2)l`