Question

For a solenoid having a primary coil of $ N_{1} $ turns and a secondary coil of $ N_{2} $ turns, the coefficient of mutual inductance is :

• A. $\mu_0\mu_r \frac{N_1N_2}{l}$
• B. $ \frac{\mu _{0}\mu _{r}N_{1}N_{2}}{Al} $
• C. $ \mu _{0}\mu _{r}N_{1}N_{2}Al $
• D. $ \frac{\mu _{0}\mu _{1}N_{1}N_{2}A}{l} $

Answer 1

Answer: (D)

Coefficient of mutual inductance $M=\frac{\phi}{I_{p}}$
$=\frac{\mu_{0} \mu_{r} N_{1} N_{2} A I_{P}}{I I_{P}}$
$=\left(\mu_{0} \mu_{r} N_{1} N_{2} A\right) / l$
where $A$ and $l$ are the length and area of cross-section respectively