Contracting Loop in a Magnetic Field

• Angie K.
In summary, the average induced emf is 8.4167*10^-2 volts and the average induced current is 1.17666*10^-2 volts.
Angie K.

Homework Statement

An elastic circular loop in the plane of the paper lies in a 0.81 T magnetic field pointing into the paper. If the loop's diameter changes from 19 cm to 6.8 cm in 0.45 s,

a. what is the magnitude of the average induced emf?

b. If the loop's resistance is 2.3 Ω, what is the average induced current I during the 0.45 s?

Homework Equations

emf = change in flux * B / change in time

magnetic flux = B*A cos Theta

The Attempt at a Solution

Using the equation from above,

the distance that I am going to use is .19m - .068m = .122 m (change in distance)

magnetic flux = (0.81T)(pi)(0.122m)^2 cos 0

= 3.7875*10^-2 T/m^2

emf = (3.7875*10^-2 T/m^2) / 0.45s = 8.4167*10^-2 Volts

Which is wrong but I am not sure where I went wrong.
Maybe something with the distance? Because I feel like that's the one place where I could have messed up...

Angie K. said:
the distance that I am going to use is .19m - .068m = .122 m (change in distance)

magnetic flux = (0.81T)(pi)(0.122m)^2 cos 0

You need to calculate the change in area, not the change in diameter.
You want this: ## \Delta A = A_{final}-A_{initial} = \pi r_{final}^2-\pi r]_{initial}^2 ##
Try that and see if it works.

Last edited:
TSny
Angie K. said:
the distance that I am going to use is .19m - .068m = .122 m (change in distance)

magnetic flux = (0.81T)(pi)(0.122m)^2 cos 0

This is where the mistake is. Try finding the initial total flux and then the final total flux (after 0.45 s). Use these to get the change in flux.

[You can ignore my post. BiGyElLoWhAt already posted]

BiGyElLoWhAt
Beat you ;)

BiGyElLoWhAt said:
Beat you ;)

BiGyElLoWhAt said:
You made a mistake here:You need to calculate the change in area, not the change in diameter.
You want this: ## \Delta A = A_{final}-A_{initial} = \pi r_{final}^2-\pi r]_{initial}^2 ##
Try that and see if it works.

BiGyElLoWhAt said:
Beat you ;)

For initial flux : .81T (pi*r (.19^2) = 9.18633e-2
For final flux: .81T (pi*r (.068^2) = 1.17666e-2

so the change in flux is 1.17666e-2 - 9.18633e-2 = - .0800967

so I plug that into find Emf:

magnitude of emf (- .0800967/0.45s) and it still isn't the right answer.

Angie K. said:
For initial flux : .81T (pi*r (.19^2) = 9.18633e-2
For final flux: .81T (pi*r (.068^2) = 1.17666e-2

so the change in flux is 1.17666e-2 - 9.18633e-2 = - .0800967

so I plug that into find Emf:

magnitude of emf (- .0800967/0.45s) and it still isn't the right answer.
Looks good except you need to interpret the word "magnitude".

TSny said:
Looks good except you need to interpret the word "magnitude".

BiGyElLoWhAt said:
Beat you ;)

I got the right answer for both parts. Thanks to you both for the help!

1. What is a contracting loop in a magnetic field?

A contracting loop in a magnetic field refers to a phenomenon in which a loop of electrically charged particles, such as plasma, is compressed and confined by the forces of a magnetic field. This can occur naturally in space, such as in solar flares, or can be artificially created in a laboratory setting.

2. How does a contracting loop form?

A contracting loop forms when a magnetic field interacts with a plasma or other electrically charged particles. The magnetic field exerts a force on the particles, causing them to move and become compressed into a loop shape. This is often accompanied by an increase in temperature and energy within the loop.

3. Why is studying contracting loops important?

Studying contracting loops is important for understanding the dynamics and behavior of magnetic fields and charged particles. This has implications for space weather, as well as for developing technologies such as nuclear fusion reactors that rely on magnetic confinement of plasma.

4. What factors affect the contraction of a loop in a magnetic field?

The contraction of a loop in a magnetic field is affected by several factors, including the strength and orientation of the magnetic field, the density and temperature of the particles in the loop, and any external forces acting on the loop. Additionally, the size and shape of the loop itself can also impact its contraction.

5. Can contracting loops be used for energy production?

Yes, contracting loops can potentially be used for energy production through the process of magnetic confinement fusion. This involves using a strong magnetic field to contain and compress plasma, causing it to release large amounts of energy. However, this technology is still in the early stages of development and is not yet a viable source of energy on a large scale.

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