Verified Solution • 2025–26 Session moderate

QJEEM20Ph685e: JEE Main 2020 Physics - Class 12 JEEM20Ph685e Solution: A long solenoid of radius R carries a time (t) - dependent…

A long solenoid of radius R carries a time (t) - dependent current
I(t)=I0t(1 - t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 ≤ t ≤ 1, the induced current (IR) and the induced EMF(VR) in the ring change as :

Multiple Choice Options

  • A Direction of IR remains unchanged and VR is zero at t = 0.25
  • B Direction of IR remains unchanged and VR is maximum at t = 0.5
  • C At t = 0.25 direction of IR reverses and VR is maximum
  • D At t = 0.5 direction of IR reverses and VR is zero

Step-by-Step Verified Solution

I(t) = I0t(1 - t)

We know, ϕ = BA

⇒ ϕ = μ0nIA

⇒ ϕ = μ0nAI0(t - t2)

Also VR = −dϕdt

= - μ0nAI0(1 - 2t)

VR = 0 when 1 - 2t = 0

⇒ t = 0.5

Also we know, VR = IRr

⇒ IR = μ0nAI0(1−2t)r

after t = 0.5, IR reverses its direction.

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