A magnetic field passes through a stationary wire loop, and its magnitude change

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 56 turns of wire and has an area of 0.20 m2. The magnetic field is oriented parallel to the normal to the loop. For purposes of this problem, this means that = 0° in Equation 22.2.

(a) For each interval, determine the induced emf.

(b) The wire has a resistance of 0.50 . Determine the induced current for the first and third intervals.
I1 = 9---Select----+ 10 11---Select---VWA
I3 = 12---Select---+- 13 14---Select---VAW

1 = 1---Select---+- 2 3---Select---VWA 2 = 4 5---Select---AVW 3 = 6---Select----+ 7 8---Select---AWV

Explanation / Answer

Induced EMF is given as

E = NBA/t

N = number of turns = 56

A = area = 0.20 m2

B/t = slope of first time interval = 0.4/0.3 = 4/3

E1 = NA (B/t) = (56 x 0.20 ) (0.4/3) = 1.493 volts

B/t = slope of second time interval = 0

E2 = NA (B/t) = (56 x 0.20 ) (0) = 0 volts

B/t = slope of third time interval = 0.2/3

E3 = NA (B/t) = (56 x 0.20 ) (0.2/3) = 0.75 volts

b)

current = I1 = E1 /R = 1.493/0.5 = 2.986 A

current = I3 = E3 /R = 0.75/0.5 = 1.5 A

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