A very long solenoid of radius R is carrying a current I(t)=(k t e)-a t(k0), as a function of time (t ≥ 0) taken as a counter clockwise current to be positive. A circular conducting coil of radius 2 R is placed in the equatorial plane of the solenoid and concentric with the solenoid itself. Then the current induced in the outer coil is correctly shown as a function of time by which of the following graph:

Question

A very long solenoid of radius R is carrying a current I(t)=(k t e)-a t(k>0), as a function of time (t ≥ 0) taken as a counter clockwise current to be positive. A circular conducting coil of radius 2 R is placed in the equatorial plane of the solenoid and concentric with the solenoid itself. Then the current induced in the outer coil is correctly shown as a function of time by which of the following graph: (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-yfkylpss1van6zxz.jpg" /> ii n d propto-(d i/d t)=-(d/d t)((α t e)-β t) =-(α e)-β t+(α t e)-β t(-β) =-(α e)-β t(1-β t) Check value at t=0

iind​∝−dtdi​=−dtd​((αte)−βt) =−(αe)−βt+(αte)−βt(−β) =−(αe)−βt(1−βt) Check value at t=0

$i_{in d} \propto - \frac{d i}{d t} = - \frac{d}{d t} ((α t e)^{- βt})$
$= - (α e)^{- βt} + (α t e)^{- βt} (- β)$
$= - (α e)^{- βt} (1 - βt)$
Check value at $t = 0$