JEE Main 2016PhysicsMagnetic Effects of CurrentMediumMCQ

JEE Main 2016Magnetic Effects of Current Question with Solution

JEE Main 2016 (10 Apr Online)

Question

A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as B=B0e-tτ, where B0 and τ are constants at time t=0. If the resistance of the loop is R, then the heat generated in the loop after a long time t is

Choose an option

Show full solutionCorrect option: B
Correct answer
Bπ2r4B022τR

Step-by-step explanation

Here, B=B0e-tτ
Area of the circular loop, A=πr2
Flux linked with the loop at any time  t ,
ϕ=BA=πr2B0e-tτ 
Emf induced in the loop, ε=-dϕdt=πr2B01τe-tτ
Net heat generated in the loop
0ε2Rdt=π2r4B02τ2R0e-2tτdt
=π2r4B02τ2R×1-2τ×e-2tτ0
=-π2r4B022τ2R×τ0-1=π2r4B022τR

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Magnetic Effects of Current chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2016, covering the Magnetic Effects of Current chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.