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Figure shows a loop falling down through a constant magnetic field which points into the screen. Due to the Lorentz Force a magnetic force is present on the top part of the wire which pushes the charge and hence a current flows. This current circulates in the loop which obeys

$\vec{J}=\sigma \vec{f}$

There is no component of magnetic force which can push the charges through the wire except from the top part of the wire. But from the above equation we know that someone has to do the pushing to make a current flow and it can't be magnetic force in this situation.

So we can say from this that an electric field exists inside the wire and this electric field points in the direction of current and makes the current flow.

The question is that ,how does this electric field come into being? and is there any electric field in the top part of the wire? Further more if the electric field points in the direction of the current, then its curl is going to be non zero!

Please help.enter image description here

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There is no induced electric field here, as $\dot{B}=0$. Charges in the top of the wire get pushed, and their displacement induces a slight variation in the electric field- a fancy way of saying that they will repel the other charges in the wire and force them to move along with the same current, $I$. After a short while, the electric field vanishes, as all of the charges move with the same current.

Just as a side note, if the loop were inside a uniform magnetic field which was changing with time, there would have been an induces electric field with nonzero curl.

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  • $\begingroup$ Current needs a force generally,as is explicit here $\vec{J}=\sigma \vec{f}$ $\endgroup$
    – Kashmiri
    Oct 18 '20 at 6:45

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