A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate `(dvecB)/(dt)`. Loop 1 of radius R `gt` r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure below. Then the emf generated is

Options

A. In loop-1 `-(dvecB)/(dt)piR^2` and in loop-2 zero
B. In loop-1 `-(dvecB)/(dt)pir^2` and in loop-2 zero
C. Zero in both loop
D. In loop-1 `-(dvecB)/(dt) pir^2` and in loop=2 -`(dvecB)/(dt) pir^2`

Answer

B

Explanation

In loop-1
`phi=vecA.vecB=AB cos theta`
`therefore` Induced emf `epsilon=(dphi)/(dt)=-(d(AB cos theta))/(dt)`
`epsilon=-A cos theta. (dB)/(dt)`
Here `vecA||vecB` hence `theta=0^@`
`therefore epsilon=-A . (dvecB)/(dt) " " [ cos 0^@=1]`
`therefore epsilon =-pir^2(dvecB)/(dt)`
For loop -2
Induced emf `epsilon=0` because loop-2 is not magnetic field .