A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate d Bdt. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure. Then the e.m.f. generated is [figure]
- zero in loop 1 and zero in loop 2
- - d Bdt r2 in loop 1 and - d Bdt r2 in loop 2
- - d Bdt R2 in loop 1 and zero in loop 2
- - d Bdt r2 in loop 1 and zero in loop 2
Answer
(4) - d Bdt r2 in loop 1 and zero in loop 2
Solution
Induced e.m.f. = - d dt, where is the flux through the loop.
Loop 1: field exists only over area r2 1 = B r2
1 = - dBdt r2
Loop 2: lies outside the field region 2 = 0 2 = 0
Answer: (4)