JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Electromagnetic Induction

A long solenoid of radius

R

carries a time (

t

) dependent current

I (t) = I_{0} t (1 - t)

. A ring of radius 2

R

is placed coaxially near its middle. During the time interval

0 \leq t \leq 1

, the induced current (

I_{R}

) and the induced EMF (

V_{R}

) in the ring changes as:

Answer: (D)

Solution

The flux linked by the ring follows the solenoid current,

ϕ = μ_{0} n I A = μ_{0} n A I_{0} t (1 - t)

, so the induced emf is

V_{R} = - \frac{d ϕ}{d t} = - μ_{0} n A I_{0} (1 - 2 t)

. This emf, and the current

I_{R}

proportional to it, pass through zero exactly at

t = 0.5

, where the sign of

(1 - 2 t)

flips. Hence at

t = 0.5

the induced current reverses direction and the induced emf is zero.

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Single correct option