A circular loop of flexible iron wire has an initial circumference of 169cm but

Question

A circular loop of flexible iron wire has an initial circumference of 169cm but its circ. is decr. at a constant rate of 15cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnetude .6T, which is oriented perpendicular to teh plane of the loop. asusme that you are facing the loop and that the magnetic field points into the loop. Find the magnitude of the emf

induced in the loop after exactly time 5.00s has passed since the circumference of the loop started to decrease.

Explanation / Answer

-15cm/s = -0.15m/s; 169cm = 1.69m;
E= -d?/dt = -d(B*S)/dt = -B*dS/dt, where S(t) is area of the loop;
S(t) =pi*r^2, while circumference p(t)=2pi*r, hence
r=p(t)/(2pi), and S(t)=pi*(p/(2pi))^2 =(0.25/pi)*p^2;
dS/dt = (0.5/pi)*p(t) *dp/dt = (0.5/pi)*p(t) *(-0.15 m/s) =
= (-0.075/pi)*p(t), m^2/s;
thus E = -B*(-0.075/pi)*p(t), where
p(t=5s) = 1.69m

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