A curious question on the inapplicability of Faraday's law

The magnetic flux is always constant during this time. However, the electric field due to the moving charges creates a time-varying magnetic flux.
  • #1
I recently came across this article on wikipedia : http://en.wikipedia.org/wiki/Faraday_paradox#Inapplicability_of_Faraday.27s_law"
In this example, the circuit does not move, and the magnetic flux through the circuit is not changing, so Faraday's law suggests no current flows. However, the Lorentz force law suggests a current does flow.

I don't understand why is it that Faraday's law is inapplicable here. But wouldn't there be a increase in magnetic flux, since the open surface will increase in area being exposed to the magnetic field. For example, if you have a circular ring of charges and you let the charges move radially outwards, then the area enclosed by this ring will increase.

So if I have a closed loop that first goes in the conducting part of the material in the direction of v X B and then through some other path to complete the loop. Then when the charges move in the direction of v, the closed loop will increase the area of the open surface exposed to B and therefore the flux increases and the current produced is exactly that as predicted using the Lorentz force law. So both laws work well... am I correct? :smile:
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  • #2
No. The electromotive force in Faraday's law is due to a change in the magnetic flux in time. The magnetic flux is the total magnetic field normal to a surface.

[tex] \mathcal{E} = - \frac{d}{dt} \int \mathbf{B}\cdot d\mathbf{S} [/tex]

The surface exposed to the magnetic field that we will be taking the flux over is constant for a given time T. This is the time between the left edge of the translating sheet just leaving the "light area" and until the right edge of the translating sheet engers the "light area." During the time that the area illuminated by the light is constant, the flux is constant since the magnetic field is a constant field applied to the same area as the light. This area does not change nor does the magnetic field, hence its time invariance. However, the movement of the sheet itself gives rise to a velocity on the electrons which must experience a Lorentz force from the magnetic field.

A better way to think of it is to assume that the translating sheet is infinitely long. So there isn't a time when the sheet enter or leaves area illuminated by the light and magnetic field.
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What is Faraday's law?

Faraday's law states that a changing magnetic field can induce an electric current in a closed circuit.

Why is there a question about the inapplicability of Faraday's law?

There is a question about the inapplicability of Faraday's law because it is based on certain assumptions and may not be applicable in all situations.

What are the limitations of Faraday's law?

Faraday's law may not hold true in cases where the magnetic field is not changing uniformly or when the circuit is not closed.

What are some examples where Faraday's law may not be applicable?

Faraday's law may not be applicable in situations such as electromagnetic induction in non-metallic materials or in the presence of strong magnetic fields.

How does the inapplicability of Faraday's law impact scientific research?

The inapplicability of Faraday's law may require scientists to use alternative theories or models to explain certain phenomena and may also lead to the development of new theories and laws.

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