Chapter 21, Problem 44P

To determine

To find the mutual inductance of an inductor.

Answer to Problem 44P

Solution:

$M_{21}={\varphi }_{21}\frac{N_2}{I_1}=\frac{{\mu }_{0}A{N}_1{N}_2}{l}$

Explanation of Solution

Number of turns = N

Length of the solenoid = l

Cross-sectional area of the solenoid = A

The magnetic flux (f)through each coil of the solenoid is given by

${\varphi }_{21}=\frac{{\mu }_0{N}_1{I}_1}{l}A=BA$

Where, B is the uniform magnetic flux inside the solenoid. Therefore, the mutual inductance can be written as

$M_{21}={\varphi }_{21}\frac{N_2}{I_1}=\frac{{\mu }_{0}A{N}_1{N}_2}{l}$