Question

$A$ $2 \,m$ long solenoid with diameter $2\, cm$ and $2000$ turns has a secondary coil of $1000$ turns wound closely near its midpoint. The mutual inductance between the two coils is

• A. $2.4 \times 10^{-4}\,H$
• B. $3.9 \times 10^{-4}\,H$
• C. $1.28 \times 10^{-3}\,H$
• D. $3.14 \times 10^{-3}\,H$

Answer 1

The Correct Option is B

Here, $l= 2 m$, diameter $= 2\, cm$ $\therefore$ radius, $ r=\frac{2}{2}=1\,cm =1\times10^{-2}\,m$ $N_{1}=2000, N_{2}=1000$ Area $=\pi r^{2}=\pi\times\left(1\times10^{-2}\right)^{2} $ $=3.14\times10^{-4}\,m^{2}$ Mutual inductance, $M =\frac{\mu_{0} N_{1}N_{2}A}{l}$ $=\frac{4\pi\times10^{-7}\times2000\times1000\times3.14\times10^{-4}}{2}$ $=3.9\times10^{-4}\,H$