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 167cm , but its circumference is decreasing at a constant rate of 12.0cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 1.00T , 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.

Find the magnitude of the emf E induced in the loop after exactly time 8.00s has passed since the circumference of the loop started to decrease. Express in Volts.

Done this 3 times already. The answer is NOT 0.014, -0.255 or 0.255. A detailed solution is appreciated.

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 167 - 8*12 = 71 cm.

= (1.00 T)(0.71/2*3.14) )(0.12 m/s)

= 0.0135 V

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