Print ViewInduced EMF and Current in a Shrinking Loop

[CoasterGT]

Induced EMF and Current in a Shrinking Loop

Homework Statement

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 170 cm, but its circumference is decreasing at a constant rate of 13.0 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 3.00 s has passed since the circumference of the loop started to decrease.

Homework Equations

C(t)= C_0 - a t .
r(t) = \frac{C(t)}{2 \pi}
\Phi(t) = \frac{B[C(t)]^2}{4 \pi}.

The Attempt at a Solution

I've done a couple things and gotten the same answer of .0187

I found the change in flux / time by multiplying the B field times the change in area/ change in time. Also tried taking the difference in flux through the given equation for phi divided by the time, but got the same result of .0187.

 

[Saketh]

$$C(t)= C_0 - a t$$

OK, this is good.

$$r(t) = \frac{C(t)}{2 \pi}$$

This is also correct.

$$\Phi(t) = \frac{B[C(t)]^2}{4 \pi}$$

Be careful. You can't just divide by time, because the area is decreasing more rapidly than the circumference (you'll kick yourself once you realize this mistake, it's that simple).

You know that (in terms of magnitudes) $$\epsilon = B \frac{dA}{dt}$$. You know A(t). The rest is just mathematics.

 

[bmanbs2]

for $$\epsilon = B \frac{dA}{dt}$$ I came up with the equation $$\epsilon = B \frac{a(at-C_0)}{2\pi}{$$. Is that correct?