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  • Define mutual inductance between a pair of coils. Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound one over the other.    

Define mutual inductance between a pair of coils. Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound one over the other.

 

 

Answers (1)

Mutual inductance is the induction of emf in a coil due to change in current in the neighbouring coil

\varepsilon =\frac{-d}{dt}(N\phi )=\frac{-MdI}{dt}

M is the coefficient of mutual induction or mutual inductance.

Let us consider two long coaxial solenoids of length 'l'

Let for solenoid S_{1}, the radius be r_{1} and for S_{2} radius be r_{2}, such that r_{1}< r_{2}

Due to the current flowing through S_{2} a magnetic flux \phi _{1} is set up in the coil S_{1}

Total flux linked with S_{1} is

N_{1}\phi _{1}=M_{12}I_{2} .............(1)

B_{2}= \mu_{o}n_{2}I_{2} is the magnetic field due to current I_{2} in S_{2}

The resulting flux linkage with the coil S_{1} is

N_{1}\phi _{1}=n_{1}l(\pi r{_{1}}^{2})\mu_{o}n_{2}I_{2}=\mu_{o}n_{1}n_{2}\pi r{_{1}}^{2}lI_{2}

Where

M_{12}=\mu_{o}n_{1}n_{2}\pi r{_{1}}^{2}l

Posted by

Safeer PP

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