Question

A magnetic field passes through a stationary wire loop, and its magnitude changes in time according to the graph in the drawing. The direction of the field remains constant, however. There are three equal time intervals indicated in the graph: 0 – 3.0 s, 3.0 – 6.0 s, and 6.0 – 9.0 s. The loop consists of 57 turns of wire and has an area of 0.12 m2. The magnetic field is oriented parallel to the normal to the loop. For purposes of this problem, this means that φ = 0˚ in Equation 22.2. (a) For each interval, determine the induced emf. (b) The wire has a resistance of 0.50 Ω. Determine the induced current for the first and third intervals.

Answer 1

The emf is given by the rate of change of flux.
The total area is 57 * 0.12
The rate of change of B is 0.4/3 , 0 , and - 0.2/3 for the three intervals.
Giving an emf of
a) 0.4 /3 * 57 * 0.12  = 0.91 V
b) zero
c) - 0.2 / 3 * 57 * 0.12 = -0.45 V

And for the current. I = V/R
so for the intervals it is
a) 0.91 / 0.50 = 1.82 A
b) zero
c) - 0.45 / 0.5 = - 0.9 A