Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10\, ext{cm}^2$ and length $20\, ext{cm}$. If one solenoid has 300 turns and the other has 400 turns, their mutual inductance is $(\mu_0=4\pi imes10^{-7}\, ext{T m A}^{-1})$ :

Question

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10\,	ext{cm}^2$ and length $20\,	ext{cm}$. If one solenoid has 300 turns and the other has 400 turns, their mutual inductance is $(\mu_0=4\pi	imes10^{-7}\,	ext{T m A}^{-1})$ :

Accepted Answer

$2.4\pi	imes10^{-4}\,	ext{H}$. For two long coaxial solenoids, $M=\mu_0\dfrac{N_1N_2A}{l}$. Here $A=10\,	ext{cm}^2=10^{-3}\,	ext{m}^2$ and $l=20\,	ext{cm}=0.2\,	ext{m}$. Substituting $N_1=300$, $N_2=400$ gives $M=4\pi	imes10^{-7}	imes\dfrac{300	imes400	imes10^{-3}}{0.2}=2.4\pi	imes10^{-4}\,	ext{H}$.

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10\,\text{cm}^2$ and length $20\,\text{cm}$. If one solenoid has 300 turns and the other has 400 turns, their mutual inductance is $(\mu_0=4\pi\times10^{-7}\,\text{T m A}^{-1})$ :

Solution

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