A 1.50 T amgnetic field (into the plane of the paper) is perpendicular to a circ

Question

A 1.50 T amgnetic field (into the plane of the paper) is perpendicular to a circuar conducting loop which is inititally at rest. Area of the loop is 4.0 cm^2

What is the induced emf in the loop?

If the conducting loop has angular rotational speed of 0.10 radian/sec and its axis of rotation is on the plane of paper as shown by the horizontal line through the diameter of the loop.

a. Calculate the change in flux linkage to its loop area in 3.0 seconds.

b. Assume that there are 150 turns, what will be the induced emf?

c. At any instant of time the loop is on the plane of the paper. What will be the direction of current in the rotating loop after very brief interval?

d. At any instant of time the loop plane is perpendicular to the plane of thepaper, i.e., it is ligned with the mgnetic field direction. What will be the direction of current in the rotating loop after a very brief time interval?

Explanation / Answer

Given that B = 1.5T

A = 4cm^2 = 4*10^-2m^2

N = 150

induced e m f e = NBAw

e = 150*1.5*4*10^-2*0.1

e = 90*10^-2V

a) t =3s

dA/dt = 4*10^-2/3 = 1.34*10^-2m^2/s

d/dt(magnetic flux) = BdA/dt cos 0 = 1.5*1.34*10^-2

magnetic flux = 2.01*10^-2wb

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