Question

A Solenoid with $N_1=1000,r_1=1cm,and{l}_1=50cm$ is concentric within a second coil of $N_2=2000,r_2=2cm$ and $l_2=50cm$ . The mutual inductance assuming free space conditions is_____ mH.

• A. 1.58
• B. 2.58
• C. 4.58
• D. 3.58

Answer 1

The correct option is A 1.58

For long coils of small cross-section, H may be assumed constant inside the coil and zero for points just outside the coil. With the first coil carrying a current $I_1$

Magnetic flux intensity, H$=\left(\frac{1000}{0.50}\right)I_1\left(A/m\right)$ (in the axial direction)

Magnetic flux density, B = ${\mu }_{o}2000I_1(Wb/m^2$)

Magnetic flux , $\varphi =BA=\left({\mu }_{0}2000I_1\right)(\pi \times 1\times {10}^{-4})\left(Wb\right)$

Since H and B are zero outside the coils , this is the only flux linking the second coil ,

$M_{12}=N_2\left(\frac{\varphi }{I_2}\right)$

$=2000\times (4\pi \times {10}^{-7})\left(2000\right)(\pi \times 1\times {10}^{-4})$

$M_{12}=1.58mH$