Print ViewInduced EMF and Current in a Shrinking Loop

In summary, we have a circular loop of flexible iron wire with an initial circumference of 170 cm, decreasing at a constant rate of 13.0 cm/s due to a tangential pull. The loop is in a uniform magnetic field of 0.600 T and we need to find the induced EMF after 3.00 s. Using the equation \epsilon = B \frac{dA}{dt}, we get the equation \epsilon = B \frac{a(at-C_0)}{2\pi}, which gives us a result of 0.0187 for the induced EMF.
  • #1
CoasterGT
6
0
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.
 
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  • #2
[tex]C(t)= C_0 - a t[/tex]
OK, this is good.
[tex]r(t) = \frac{C(t)}{2 \pi}[/tex]
This is also correct.
[tex]\Phi(t) = \frac{B[C(t)]^2}{4 \pi}[/tex]
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) [tex]\epsilon = B \frac{dA}{dt}[/tex]. You know A(t). The rest is just mathematics.
 
  • #3
for [tex]\epsilon = B \frac{dA}{dt}[/tex] I came up with the equation [tex]\epsilon = B \frac{a(at-C_0)}{2\pi}{[/tex]. Is that correct?
 

1. What is Print View-Induced EMF?

Print View-Induced EMF (electromotive force) refers to the phenomenon in which a changing magnetic field induces an electric current in a closed loop or circuit. This is also known as Faraday's Law of Induction.

2. How does a shrinking loop affect Print View-Induced EMF?

A shrinking loop will experience an increase in the magnetic flux passing through it, which in turn will increase the induced EMF. This is because the changing area of the loop causes a change in the magnetic field, leading to a higher induced current.

3. What factors affect the magnitude of Print View-Induced EMF?

The magnitude of the induced EMF is affected by the rate of change of the magnetic field, the number of turns in the loop, and the size and shape of the loop. Additionally, the material of the loop and the resistance of the circuit can also impact the magnitude of the induced current.

4. How does Lenz's Law relate to Print View-Induced EMF?

Lenz's Law states that the direction of the induced current is always such that it opposes the change in the magnetic field that caused it. This means that the induced current in a shrinking loop will flow in a direction that creates a magnetic field that opposes the change in the original magnetic field.

5. What are some real-life applications of Print View-Induced EMF?

Print View-Induced EMF has many practical applications, such as in electrical generators, transformers, and induction cooktops. It is also used in devices such as microphones and speakers, which convert sound waves into electrical signals. Additionally, Print View-Induced EMF is the basis for many electric motors and can be harnessed for wireless charging of devices.

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