A very long solenoid of radius R is carrying current I t = k t e - α t k 0 , as a function of time t ≥ 0 . Counterclockwise current is taken to be positive. A circular conducting coil of radius 2 R

Question

A very long solenoid of radius R is carrying current I t = k t e - α t k > 0 , as a function of time t ≥ 0 . Counterclockwise current is taken to be positive. A circular conducting coil of radius 2 R is placed in the equitorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by:

TestHub · Accepted Answer

ϕ o u t e r = μ 0 n K t e - α t 4 π R 2 ε = - d ϕ d t = - μ 0 n K 4 π R 2 ( e - α t 1 - α t ) i i n d u c e d = - c e - α t 1 - α t R e s i s t a n c e At t = 0 , I i n d u c e d = - v e From the above equation and initial value of current we can say the correct graph is B.

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