A rectangular loop of wire 0.75 m long and 0.60 m wide moves at 12 m/s into a re

Question

A rectangular loop of wire 0.75 m long and 0.60 m wide moves at 12 m/s into a region of uniform magnetic field 2.5 T. The induced current is 3.0 A, counterclockwise. The field is directed (into/out of) the page. (a) Calculate the emf, the electrical resistance of the loop, and the force on its leading edge needed to keep it moving. epsilon = R = F = (b) Calculate the increase in the magnetic flux during a .01-second interval Delta Phi_ = Wb (c) During the same interval calculate the work W done by the force in part (a), and (separately) calculate the electrical energy U supplied to the circuit by the emf, demonstrating the expected relationship: W = U = (d) The loop is now wholly within the field region. Find the current (i) if B is spatially uniform ANS: (ii) if B is nonuniform, now having value 3.0 T at the loop's leading edge vs 2.5 T at the trailing edge. (Use the value of R in part (a).) ANS:

Explanation / Answer

a)

Emf generated :

E = BLv

So, current , I = E/R = BLv/R = 3

So, 2.5*0.75*12/R = 3

So, R = 6 ohm <------- answer

force on its leading edge = F = BId = 2.5*3*0.6 = 4.5 N <------ answer

Emf, E = I*R = 3*6 =18 V <---------answer

b)

Increase in magnetic flux = I*R*t = 3*6*0.01 = 0.18 T

c)

Work done = F*v*t = 4.5*12*0.01 = 0.54 J

U = V*I*t = 18*3*0.01 = 0.54 J

d)

current = 0 <---- as no change in flux occurs

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