Question

A solenoid of length $30\, cm$ with $10$ turns per centimetre and area of cross-section $40\, cm^{2 }$ completely surrounds another co-axial solenoid of same length, area of cross-section $20 \,cm^{2}$ with $40$ turns per centimetre. The mutual inductance of the system is

• A. $10\,H$
• B. $8\,H$
• C. $3\, mH$
• D. $30\, mH$

Answer 1

Answer: (C)

Mutual inductance of the system,
$M=\mu_{0}n_{1}n_{2}A_{2}l$
where $A_{2}$ is the area of inner solenoid
$n_{1}=10\,cm^{-1}=1000\, m^{-1}$
$n_{2}=40\,cm^{-1}=4000\,m^{-1}$
$l=30\,cm=30\times 10^{-2}\, m$
$A_{2}=20\,cm^{2}=20\times 10^{-4}\,m^{2}$
$\therefore M=4\pi \times10^{-7}\times1000\times4000\times20\times10^{-4}\times30\times10^{-2}$
$=301.44\times10^{-5}\,H=3\,mH$