A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate `(dB)/(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 figure. Then, the emf generated is

Options

A. `-(dvecB)/(dt) pi R^2` in loop 1 and zero in loop 2
B. `-(dvecB)/(dt) pi r^2` in loop 1 and zero in loop 2
C. Zero in loop 1 and zero in loop 2
D. `-(dvecB)/(dt) pi r^2` in loop 1 and `-(d vecB)/(dt) pi r^2` in loop 2

Answer

B

Explanation

For Loop 1
`epsilon _("ind") = (- d phi)/(dt) = -A ((dB)/(dt)) cos 0^@ = - pi r^2 ((dB)/(dt))`
`A = pi r^2` as B is restricted with in radius r.
For Loop 2, `epsilon_("ind") = 0` as no flux linkage.