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Two long co-axial solenoids have radii, ...

Two long co-axial solenoids have radii, and number of turns per unit length equal to `r_(1), r_(2)` and `n_(1), n_(2)` respectively where suffix 1 refers to the outer solenoid and 2 refers to the inner solenoid. Length of both is l. The current in the outer solenoid is made to grow as `I_(1) = kt` where t is time. Resistance of the wire used in inner solenoid is R. Write the current induced in the inner solenoid assuming that it is shorted.

Text Solution

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The correct Answer is:
`i=(kpi mu_(0)n_(1)n_(2)r_(2)^(2)l)/(R) (1-e^(-t//tau))` where `tau = (pi mu_(0)n_(2)^(2) r_(2)^(2)l)/(R)`
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