Item 10 Shrinking Loop. A circular loop of flexible iron wire has an initial cir

Question

Item 10 Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 166cm, but its circumference is decreasing at a constant rate of 130cm/s due to a tangential pull on the wire The loop is in a constant uniform magnetic field of magnitude 0.500 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 initial Find the magnitude of the emf Epsilon induced in the loop after exactly time 2.00s has passed since the circumference of the loop started to decrease. Express your answer numerically in volts to three significant figures. Epsilon= .017 V A Message from Your Instructor: For Item 10, be sure to find the rate at which the area is changing. You may first want to find the rate at which the circumference changes (dC/dt) and use that to find the rate at which the radius is changing (dr/dt).

Explanation / Answer

Initial circumaference = 2*pi*r1

166 = 2*pi*r1

==> r1 = 166/(2*pi)

= 26.42 cm (initial radius of the loop)

afer two seconds,

final circumaference = 2*pi*r2

166 - 2*13 = 2*pi*r1

==> r2 = 140/(2*pi)

= 22.3 cm

induced emf = B*dA/dt

= B*2*pi*r2*dr/dt (A = pi*r^2 ===> dA/dt = 2*pi*r*dr/dt)

= 0.5*2*pi*0.223*0.13

= 0.091 volts<<<<<<<<--------------Answer

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