Question

A loop of wire sits in a uniform magnetic field, everywhere pointing toward you. Due to a changing magnetic flux through the loop, an induced current flows in the wire, clockwise as shown. The area of the loop is J. 1.63 m2 , and the magnetic field initially has magnitude K. 0.61 T.

(a) Suppose that, over a time period of L. 1.47 s, the magnetic field changes from its initial value, producing an average induced voltage of M. 8.7 V. What is the final value of the magnetic field after this time period? Answer: _____________.___ T

(b) Now let’s set the magnetic field back to its starting magnitude of K. 0.61 T, and assume we achieve the same induced voltage of M. 8.7 V over a time period of L. 1.47 s by keeping the magnetic field fixed but changing the area of the wire loop. What is the final value of the loop’s area after this time period? Answer: ____________.___ m2

(c) OK, back to the starting point… the loop once again has its original area of J. 1.63 m2 , and the magnetic field has its original magnitude of K. 0.61 T. This time we’re going to achieve the same induced voltage of M. 8.7 V by rotating the loop through a 90o angle. How much time must it take for the loop to complete this 90o turn? Answer: _____________.__ s

Answer 1

Given Data

Magnetic Field, B2 = 0.61 T.

EMF , E = 8.7 V

Time, t = 1.47 s

Area, A = 1.63 m²

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a) Here the induced current is clockwise, the magnetic field should be increased.

induced emf = A*(B2 - B1)/t

emf*t/A = B2 - B1

==> B2 = B1 + emf*t/A

==> B2 = 0.61+ 8.7*1.47/1.63

==> B2 = 8.46 T

b) Here the induced current is clockwoise, the Area of the loop should be increased.

induced emf = B*(A2-A1)/t

emf*t/B = A2-A1

==> A2 = A1 + emf*t/B

==> A2 = 1.63 + 8.7*1.47/0.61

==> A2 = 22.6 m²

c) emf = change in magnetic flux/time

    emf = (A1*B1 - 0)/t

     t = A1*B1/emf

     t = 1.63*0.61 / 8.7

     t = 0.114 s