Question

A circular coil with a cross-sectional area of $4{cm}^2$ has $10$ turns. It is placed at the center of a long solenoid that has $15$ turns/cm and a cross-sectional area of $10{cm}^2$, as shown in the figure. The axis of the coil coincides with the axis of the solenoid. What is their mutual inductance?

• A. $7.54\mu H$
• B. $8.54\mu H$
• C. $9.54\mu H$
• D. $10.54\mu H$

Answer 1

The correct option is A $7.54\mu H$

Given : Number of turns in coil $N_2=10$

Number of turns per unit length in solenoid, $n=15$ per cm $=1500$ turns per meter

Area of the coil $A_2=4$ $c{m}^2=4\times {10}^{-4}$ $m^2$

Mutual inductance $M={\mu }_{o}n{N}_2{A}_{2}cos\theta$, where $\theta$ is the angle between $\overrightarrow{B}$ and $\overrightarrow{A_2}$

$\therefore$ $M=4\pi \times {10}^{-7}\times 1500\times 10\times 4\times {10}^{-4}\times 1$ $(\because \theta =0^o)$

$⟹M=7.54\times {10}^{-6}H=7.54\mu H$