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A long solenoid of radius a and number o...

A long solenoid of radius a and number of turns per unit length n is enclosed by cylindrical shell of radius R. Thickness d(dltltR) and length L. A variable current `i=i_(0) sin omega t` flows through the coil. If the resistivity of the material of cylindrical shell is `(rho)`, find the induced current in the shell.

Text Solution

Verified by Experts

The correct Answer is:
`I=((mu_(0)ni_(0)omega cosomegat)pia^(2)(Ld))/(rho2piR)`
Flux through cylindrical shell =mu_(0)nipia^(2)
`phi=mu_(0) nipia^(2)`
`e=|(dphi)/(dt)|= mu_(0)npia^(2)(di)/(dt) sin omegat=mu_(0)npia^(2)omegai_(0) cosomegat`
`=(mu_(0)ni_(0)omega cosomegat)pia^(2) ...(1)`
`I=e/R and R=rho.l/A, I=(eA)/(rhol)...(2)`
From `(1)` and `(2)`
`I=((mu_(0)ni_(0)omega cosomegat)pia^(2)(Ld))/(rho.2piR)`
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