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 162cm , but its circumference is decreasing at a constant rate of 13.0cm/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 EMF induced in the loop after exactly time 1.00s has passed since the circumference of the loop started to decrease. Express your answer numerically in volts to three significant figures.

Explanation / Answer

-13cm/s = -0.13m/s;

162cm = 1.62m;
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) *(-0.13 m/s) =
= (-0.065/pi)*p(t), m^2/s;
thus E = -B*(-0.065/pi)*p(t), where
p(t=1s) = 1.62m –(0.13 m/s)*(1 s) =1.49m;
E= -1 * (-0.065/pi) *1.49 =0.03084 V;
E = 30.8 mV;

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.