Question

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 167 cm, but its circumference is decreasing at a constant rate of 10.0 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.

Find the (magnitude of the) emf EMF induced in the loop after exactly time 1.00 s has passed since the circumference of the loop started to decrease.
im pretty sure ive been doing it right but as usual probaly a dumb mistake.

Answer 1

Area A is related to circumference C by

A = pi r^2 = pi * [C/(2 pi)]^2
= [1/(4 pi)]C^2

C = 1.67 - 0.1 t (in meters)
dA/dt = [1/(2 pi)] C dC/dt
= -(0.05/pi) C

V(t) = B*dA/dt = B (0.05/pi) C(t)
With B in Tesla, the answer will be in volts. Choose t = 1 second to get C. I have thrown out the minus sign, since we don't care about polarity

Check my math and thoughts. No guarantees here.

Answer 2

it all looks right and what i did also. yet it seems like the answer should be larger because whenever i input it into the program it seems like its too small because it says the flux should occur since the area is changing. It seems to be taking it as zero. we converted it to meters so it should be ok.

Answer 3

nvm dangit it works. just off by a small amount.

Answer 4

Spencer is wrong. Just so you guys know

Answer 5

@drwls math mustve been different in 2008 because i have no idea what you did