Question

A straight solenoid of length $1\text{m}$ has $5000$ turns in the primary and $200$ turns in the secondary. If the area of cross-section is $4{\text{cm}}^2$, the mutual inductance between primary and secondary will be

• A. $50.2\text{H}$
• B. $502\mu \text{H}$
• C. $502\text{mH}$
• D. $5.02\text{H}$

Answer 1

The correct option is B $502\mu \text{H}$

Mutual induction between two coils of same area of cross-section and length is,

$M=\frac{{\mu }_0{N}_1{N}_{2}A}{l}$

Substituting the data given in the question,

$M=\frac{4\pi \times {10}^{-7}\times 5000\times 200\times 4\times {10}^{-4}}{1}$

$M=16\times 3.14\times {10}^{-5}=502\times {10}^{-6}=502\mu \text{H}$

Hence, option (b) is the correct answer.