Question

A plane spiral with a great number N of turns wound tightly to one another is located in a uniform magnetic field perpendicular to the spiral's plane. The outside radius of the spiral's turns is equal to a. The magnetic induction varies with time as B = B₀ sin ωt, where B₀ and ω are constants. Find the amplitude of emf induced in the spiral.

Answer 1

The flat shape is made up of concentric loops, having different radii, varying from 0 to a. 

Let us consider an elementary loop of radius r, then e.m.f. induced due to this loop

and the total induced e.m.f.,

.......(1)

where π r² ω cos ωt is the contribution of one turn of radius r and dN is the number of turns in the interval [r, r + dr].