JEE Main · 2019 · 09 Apr 2019 · Shift 2 · Electromagnetic Induction

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 \geq 0

). counter clockwise current is taken 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. The current induced in the outer coil is correctly depicted, as a function of time, by:-

(A)(see structure)
(B)(see structure)
(C)(see structure)
(D)(see structure)
✓ Correct

Answer: (D)

Solution

The field inside the solenoid is proportional to

I (t) = k t e^{- α t}

, so the flux the outer coil links follows the same shape, and the induced current is proportional to

- \frac{d I}{d t}

. Differentiating,

\frac{d I}{d t} = k e^{- α t} (1 - α t)

, which is positive before

t = \frac{1}{α}

and negative after it. The induced current therefore starts with one sign at

t = 0

, falls to zero exactly at

t = \frac{1}{α}

where

\frac{d I}{d t}

changes sign, reverses, and then decays back to zero as

t \to \infty

. The graph showing this single sign reversal, with a zero-crossing at

t = \frac{1}{α}

and a decay to zero, is the one that fits.

JEE Main · 2019 · 09 Apr 2019 · Shift 2 · Single correct option

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JEE Main · 2019 · 09 Apr 2019 · Shift 2 · Electromagnetic Induction

Solution

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