A question about Faraday's law

In summary, the current through the coil in the picture generates a force on the ring which repells it.
  • #1
LiorE
38
0
My question is about the system in the picture. There is an upwards force which acts on the ring. My problem is that I don't see how it comes about. I mean, suppose that at time t, the current through the coil flows counterclockwise and is increasing. So there is an increasing, upward pointing magnetic field through the ring. That should induce a current on it in a clockwise direction. But then, according to the Lorentz force equation, the force on the ring should be sideways, isn't it? I mean it dosen't make sense that the force will be in the same direction as the magnetic field anyway, because [tex]\vec F = q(\vec{v} \times \vec{B})[/tex], so it has to be perpendicular to both v and B.

So how is that force created?

Thanks in advance,

Lior
 

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  • #2
This should give you an idea:
http://img253.imageshack.us/img253/3589/76749370cc6.png [Broken]

(sorry for the ugly sketch, any reference to a sketch making program would be appreciated =x )
 
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  • #3
Oh, I get it - because B has a component parallel to the ring. Thanks!
 
  • #4
k3d
"google sketchup"
 
  • #5
LiorE said:
Oh, I get it - because B has a component parallel to the ring. Thanks!

No... B has a components perpendicular to the ring. In the region of the ring, B has both radial and axial components.
 
  • #6
This is actually a very interesting question, guys.

With an infinitely long core, the B field will be purely axial, following along the core. the Lorenz force on the charges moving in the ring are anti-radial--directed inward. So is the ring repelled in this case?? I don't think so. There's no preferred axial direction. But at the end of the core, or the end of a solenoid, the field diverges outward, radially. This would seem to be the cause for the ring being repelled.

Remember, this only works for an AC current in the coil. From what I can deduce, the changing flux passing through the ring induces a circumpherential electric field inducing a current in the loop. But the radial component of the magnetic field in the region of the ring acts under the Lorentz force,

F_z = q v_phi B_r

to push the ring away.

Any Yays, or Nays, your just another lunatic on the internet?
 
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1. What is Faraday's law?

Faraday's law, also known as Faraday's law of induction, is a fundamental principle of electromagnetism that describes the relationship between a changing magnetic flux and an induced electromotive force (EMF) in a conducting loop or coil.

2. Who is Michael Faraday and why is this law named after him?

Michael Faraday was a British scientist and chemist who made significant contributions to the fields of electricity and magnetism. He is credited with discovering the principle of electromagnetic induction, which led to the development of Faraday's law. This law is named after him as a tribute to his groundbreaking work in the field of electromagnetism.

3. What is the formula for Faraday's law?

The mathematical formula for Faraday's law is:
EMF = -N(dΦ/dt)
where EMF is the induced electromotive force, N is the number of turns in the coil, and dΦ/dt is the rate of change of magnetic flux through the coil.

4. How is Faraday's law used in practical applications?

Faraday's law has many practical applications, including electric generators, transformers, and induction motors. It is also the basis for technologies such as wireless charging and electromagnetic braking in trains and roller coasters.

5. What is the connection between Faraday's law and Lenz's law?

Lenz's law is a consequence of Faraday's law, which states that the direction of the induced current in a circuit will always be such that it opposes the change that caused it. In other words, Lenz's law is a result of the conservation of energy and is a direct consequence of Faraday's law of induction.

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