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 169cm , but its circumference is decreasing at a constant rate of 15.0cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.700T , 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

Find the magnitude of the emf E induced in the loop after exactly time 9.00s has passed since the circumference of the loop started to decrease.

Part A Find the magnitude of the emf E induced in the loop after exactly time 9.00s has passed since the circumference of the loop started to decrease. Express your answer numerically in volts to three significant figures.

Explanation / Answer

From the wording of the problem, it's not the average rate of change of area over the 0 - 5 s interval that you want, it's the current rate of change of area at t = 9 s.
First calculate r, dr/dt and dA/dt.
dr/dt = -0.15/(2pi) = -2.38732414637843E-02 m/s
circumference C = C0-t*dC/dt = 1.7-9*0.15 = 0.35 m
dA/dt = dr/dt*C = -2.26795793905951E-02 m^2/s.
Finally V = d(BA)/dt = B*dA/dt = 1.58757053030549E-02 V. (answer)
EDIT: I decided to work this out, just being curious, so numbers are added. Also removed a bunch of unnecessary stuff (computing r0, dr/dt and r to find C).
To visualize why dA/dt = dr/dt*C, think of unrolling C to a straight line and adding another line a distance dr directly above it. The area enclosed, dr*C, is dA.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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