Question

Three identical conducting circular loops are placed in uniform magnetic fields. Inside each loop,there are two magnetic field regions, separated by dashed line that coincides with a diameter, as, shown. Magnetic fields may either be increasing (marked as INCR) or decreasing (marked as DECR) in magnitude at the same rates.If $I_A,I_B\text{and}{I}_C$ are the magnitudes of the induced currents in the loops $A,B\text{and}C$ respectively then choose the CORRECT relation :

• A. $I_A>I_B=I_C$
• B. $I_A=I_C>I_B$
• C. $I_A=I_B=I_C$
• D. $I_C>I_A>I_B$

Answer 1

The correct option is B $I_A=I_C>I_B$

Given :Three identical conducting circular loops are placed in uniform magnetic fields. Inside each loop,there are two magnetic field regions, separated by dashed line that coincides with a diameter, as, shown. Magnetic fields may either be increasing (marked as INCR) or decreasing (marked as DECR) in magnitude at the same rates.IA,IB and ICIA,IB and IC are the magnitudes of the induced currents in the loops A,B and CA,B and C respectively.

Solution :

According to the Faraday's law whenever magnetic flux passing through a loop changes there is an EMF produced in loop that opposes the change in flux.

$E=-\frac{d\varphi }{dt}$

Case of Loop -A

Since magnetic field is out of the plane and continuously increasing in both parts so IA will be clockwise and increasing.

Case of Loop -B

Since in upper part magnetic field is out of the plane and increasing so current I will be clockwise and increasing according to Faraday's law while in lower part magnetic field is out of the plane and decreasing current will be increasing in anticlockwise direction so net IB will be decreasing.

Case of Loop-C

In upper part magnetic field is out of the plane and decreasingcurrent will be increasing in anticlockwise direction while lower part magnetic field is inside the plane and increasing so current will be increasing in anticlockwise direction so net current IC will be increasing

The Correct Opt:B