- #1
DocZaius
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Consider a charge in free space. There is initially no magnetic field and the only electric field is the one caused by the charge. Now introduce a B field which increases with time:
[itex]\vec{B}=B\:t\:\hat{z}[/itex]
Faraday's Law:
[itex]\nabla\times\vec{E}=-\frac{\partial\vec{B}}{\partial t}[/itex]
states that a curling electric field would be induced. The integral form of the law would imply that for any loop I choose in the x-y plane, there would be a changing magnetic flux through it and thus a curling electric field around it. But for any loop whose right edge I place on the charge to apply some electric force to it, I can choose an identically sized loop whose left edge is also on the charge. By symmetry there should be no force on the charge in the x or y direction. But since the x-y plane and those parallel to it are the only planes through which there is changing magnetic flux, then it would have been the only plane on which the charge could have had an electric field applied to it. Since there is none there, and I see no reason to accelerate the charge in the z direction, is it safe for me to say the charge is not accelerated?
edit: Just want to make clear that I know the magnetic field itself would do no work. My question really is if the induced electric field from the changing magnetic field is doing any work.
[itex]\vec{B}=B\:t\:\hat{z}[/itex]
Faraday's Law:
[itex]\nabla\times\vec{E}=-\frac{\partial\vec{B}}{\partial t}[/itex]
states that a curling electric field would be induced. The integral form of the law would imply that for any loop I choose in the x-y plane, there would be a changing magnetic flux through it and thus a curling electric field around it. But for any loop whose right edge I place on the charge to apply some electric force to it, I can choose an identically sized loop whose left edge is also on the charge. By symmetry there should be no force on the charge in the x or y direction. But since the x-y plane and those parallel to it are the only planes through which there is changing magnetic flux, then it would have been the only plane on which the charge could have had an electric field applied to it. Since there is none there, and I see no reason to accelerate the charge in the z direction, is it safe for me to say the charge is not accelerated?
edit: Just want to make clear that I know the magnetic field itself would do no work. My question really is if the induced electric field from the changing magnetic field is doing any work.
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