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 163 cm , but its circumference is decreasing at a constant rate of 11.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.600 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

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

Part B

Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.

Explanation / Answer

C = 2r
At t =9 s,
168 cm - (11.0 cm/s)(9.00 s) = 2r
r = 9.70 cm

dC/dt = 2(dr/dt)

A = r²
dA/dt = 2r(dr/dt)
dA/dt = r(dC/dt)
dA/dt = (9.70 cm)(-11.0 cm/s)
dA/dt = -106.7 cm²/s

= -d/dt
= -B dA/dt
= -(1.00 T)(-115 cm²/s)(m² / 100² cm²)
= 1.15e-2 V

2.Since the area of the loop is decreasing, the flux is decreasing; hence, the induced current acts to increase the flux (per Lenz's law). Looking along the field into the loop and utilizing the right hand rule, we see that the current must be clockwise to counteract the decrease in flux.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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