Contracting Loop in a Magnetic Field (emf and current)

• GDGirl
In summary, the problem is asking for the magnitude of the average induced emf and the average induced current in a circular loop with a changing diameter in a magnetic field. To solve, we use Faraday's Law and evaluate the rate of change of magnetic flux through the loop. The correct equation for the change of area is \pi R_i^2 - \pi R_f^2.
GDGirl

Homework Statement

An elastic circular loop in the plane of the paper lies in a 0.71 T magnetic field pointing into the paper. If the loop's diameter changes from 19.3 cm to 7.2 cm in 0.54 s,

a. what is the magnitude of the average induced emf?
HELP: Use Faraday's Law and evaluate the rate of change of magnetic flux through the loop.

b. If the loop's resistance is 2.6 Ω, what is the average induced current I during the 0.54 s?

Homework Equations

$$\Delta$$$$\Phi$$/$$\Delta$$t=emf
$$\Delta$$$$\Phi$$=magnetic flux = BAcos$$\theta$$

The Attempt at a Solution

So I used the above equation to find the emf
$$\pi$$(.0605)2(.71)/.54 = .0151
Where the value for r is the amount that the radius changes in the time given.
This is wrong, and I'm not quite sure what else to try...

GDGirl said:

Homework Statement

An elastic circular loop in the plane of the paper lies in a 0.71 T magnetic field pointing into the paper. If the loop's diameter changes from 19.3 cm to 7.2 cm in 0.54 s,

a. what is the magnitude of the average induced emf?
HELP: Use Faraday's Law and evaluate the rate of change of magnetic flux through the loop.

b. If the loop's resistance is 2.6 Ω, what is the average induced current I during the 0.54 s?

Homework Equations

$$\Delta$$$$\Phi$$/$$\Delta$$t=emf
$$\Delta$$$$\Phi$$=magnetic flux = BAcos$$\theta$$

The Attempt at a Solution

So I used the above equation to find the emf
$$\pi$$(.0605)2(.71)/.54 = .0151
Where the value for r is the amount that the radius changes in the time given.
This is wrong, and I'm not quite sure what else to try...

For the change of area, you must use : $\pi R_i^2 - \pi R_f^2$
where Ri and Rf are the initial and final radii.
I see what you did (you took the difference of diameter and divided this by 2 to get a radius ) but that does not give the correct change of area.

Oh, that makes sense. Thanks!

1. What is contracting loop in a magnetic field?

A contracting loop in a magnetic field refers to the phenomenon in which a closed loop of conducting material, such as a wire, experiences a change in size or shape when exposed to a magnetic field. This change in size or shape is caused by the interaction between the magnetic field and the electric current flowing through the loop.

2. How does a contracting loop generate an emf?

The changing magnetic field around a contracting loop induces an electric field within the loop, which in turn creates an electromotive force (emf). This emf causes electric charges to flow through the loop, resulting in an electric current.

3. What factors affect the strength of the current induced in a contracting loop?

The strength of the current induced in a contracting loop depends on several factors, including the strength of the magnetic field, the rate at which the loop contracts, the size and shape of the loop, and the material of the conducting loop.

4. How does Lenz's law relate to contracting loops in a magnetic field?

Lenz's law states that the direction of the induced current in a closed loop will always oppose the change in the magnetic flux that caused it. In the case of a contracting loop, this means that the induced current will flow in such a way that it produces a magnetic field that opposes the original changing magnetic field, thus creating a resistance to the contraction of the loop.

5. Can a contracting loop in a magnetic field be used to generate electricity?

Yes, a contracting loop in a magnetic field can be used to generate electricity. This phenomenon is used in devices such as generators and transformers, where the changing magnetic field induces an emf in a conducting loop, which can then be used to produce an electric current.

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