Shrinking Loop. A circular loop of flexible iron wire has an initial circumferen

Question

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 167 cm , but its circumference is decreasing at a constant rate of 10.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 1.00 T , which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.

Part A

Find the magnitude of the emf E induced in the loop after exactly time 7.00 s has passed since the circumference of the loop started to decrease.

Part B

Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.

Explanation / Answer

A)We know that induced emf is given by

e = d(phi)/dt

phi = B.dA = BA = pi r^2 B

e = pi r^2 B/dt = pi B 2 r (dr/dt)

e = -B C(t) dr/dt

C is the circumference of the circle

C(t) = C0 + (dC/dt)t

C(t) = 1.67m - (0.1m/s)t

dr/dt = 1/2 pi (dC/dt) = -(0.1/2pi)t

putting in eqn of induced emf

e (at t = 7s) = B [C0 + (dC/dt)t ] (dr/dt)

e = -1 (1.67 - 0.1 x 7)(-0.1/2 pi) = 1.5 x 10^-2 V

Hence, e = 1.5 x 10^-2 V

B)The direction of induced current would be clockwise. The flux is decreasing in the loop, the current try to appose the change.

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