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 169 cm, but its circumference is decreasing at a constant rate of 15.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.700 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. Find the magnitude of the emf epsilon induced in the loop after exactly time 7.00 s has passed since the circumference of the loop started to decrease. Express your answer numerically in volts to three significant figures. epsilon = 10.9 V

Explanation / Answer

Co = 169 cm , dC/dt = 15 cm/s

B = 0.7 T , t = 7 s

from faradays induced emf V = d(phi)/dt

V = d(B*pi*r^2)/dt

V = pi*B*2r*dr/dt= BC(t)(dr/dt) ..(1)

Note that the information gives us equation for the circumference of the circle C and the derivative of r:

C(t) = Co+(dC/dt)*t

C(t) = 1.69 -(0.15)t

dr/dt = (1/2pi)(dC/dt) = -0.15/2pi

from (1)

V = B(Co +(dC/dt)t)(dr/dt)

V = (0.7)(1.69 - 0.15*7)(0.15/(2*3.14))

V = 10.7*10^-3 = 0.0107 V

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