Question

A long solenoid of length $L$, cross section $A$ having $N_1$ turns has wound about its centre with a small coil of $N_2$ turns as shown in Fig. The mutual inductance of two circuits is:

• A. $\frac{{\mu }_{0}A\left(N_1/N_2\right)}{L}$
• B. $\frac{{\mu }_{0}A\left(N_1{N}_2\right)}{L}$
• C. ${\mu }_{0}A{N}_1{N}_{2}L$
• D. $\frac{{\mu }_{0}A{N}_1^2{N}_2}{L}$

Answer 1

Answer: (B)

$\frac{{\mu }_{0}A\left(N_1{N}_2\right)}{L}$

${\varphi }_2=N_2{B}_{1}A$
${\varphi }_2=N_2\times \frac{{\mu }_0{N}_1{I}_1}{L}\times A$
${\varphi }_2=\frac{{\mu }_0{N}_1{N}_{2}A}{L}{I}_1$
Comparing with: ${\varphi }_2=M{I}_1$
We get: $M_2=\frac{{\mu }_0{N}_1{N}_{2}A}{L}$