A solenoid of length 30 cm with 10 turns per centimetre and area of cross -section $40 \mathrm{~cm}^

Question

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

Professor PC Thomas Classes · Answer

Mutual inductance of the system\ $\mathrm{M}=\mu_{0} \mathrm{n}_{1} \mathrm{n}_{2} \mathrm{~A}_{2} \ell$\ Where $A_{2}$ is the area of inner solenoid\ $\mathrm{n}_{1}=10 \mathrm{~cm}^{-1}=1000 \mathrm{~m}^{-1}$\ $\mathrm{n}_{2}=40 \mathrm{~cm}^{-1}=4000 \mathrm{~m}^{-1}$ $$ \begin{aligned} & \quad \ell=30 \mathrm{~cm}=30 	imes 10^{-2} \mathrm{~m} \ & \mathrm{~A}_{2}=20 \mathrm{~cm}^{2}=20 	imes 10^{-4} \mathrm{~m}^{2} \ & 	herefore \mathrm{M}=4 \pi 	imes 10^{-7} 	imes 4000 	imes 1000 	imes 20 	imes 10^{-4} 	imes 30 	imes 10^{-2}=301.44 	imes 10^{-5}=3 \mathrm{mH} \end{aligned} $$