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 160cm , but its circumference is decreasing at a constant rate of 15.0cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.800T , 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 9.00s has passed since the circumference of the loop started to decrease.

Express your answer numerically in volts to three significant figures.

Part B

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

Explanation / Answer

induced emf e = dphi /dt

so we need an expression for phi = BA = Bpi r^2

and since circumference C = 2 pi r,

we can write that as phi = BA = B* pi (C^22/4 pi^2 2)

phi   = BC^2/ 4pi

Therefore d phi /dt = (BC/2pi ) (dC/dt)

since we know C is a function of t.

after 8 seconds, the circumference is 160 - 9*15 = 25 cm.

= (0.8)(0.25/2*3.14) )(0.15)

= 0.00477 V   or 4.77 mV
-----------------------------------------------

induced current I = emf/R

direction is clcokwise

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