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Consider the following arrangement-enter image description here

We have a conducting sphere and a positively charged infinite sheet on the left. The field creates induced charges and the net electric field inside the conductor is zero after a very short time. During this short time, there is a current in the conductor as electrons as dragged opposite to the external electric field.

My teacher says that if we want to sustain this brief current we should connect it with a conducting wire making a closed loop. The electrons will flow anticlockwise giving a steady current, which I think is wrong.

When we connect the conducting wire, the sphere and the wire become one complete metal and after a short time again, there will be induced charges in this big metal and electrostatic condition will be reached. The potential inside will be the same everywhere so how will the current flow in a closed loop?

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    $\begingroup$ Your teacher is wrong. Even if there weren't induced charges in the wire, the electric field produced by the charges opposes any electric field created by the plate. $\endgroup$
    – gmz
    Oct 6, 2021 at 6:47
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    $\begingroup$ As @gmz already said, your teacher is wrong. If it were the case, you could build a perpetual motion machine with it. $\endgroup$
    – Mechanic
    Oct 6, 2021 at 8:51
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    $\begingroup$ What if both the sphere and the wire are superconducting? Why should the induced current stop after a short (or long, given zero resistivity) time? $\endgroup$ Oct 13, 2021 at 10:40
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    $\begingroup$ Oh no, you need to get a new teacher... $\endgroup$
    – knzhou
    Oct 13, 2021 at 21:02

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There is really not much to add to the comments. Why are the charges separated on the two sides of the sphere? because there is an electric field that pushes the negative charges to the left and the positive to the right, right? This field is produced by the charge on that infinite sheet. This field exists not only in the space occupied by the sphere but everywhere. If you have another piece of metal in this space you will see the same effect, negative charges pushed to the left hand side, the side nearest to the infinite sheet. So another piece of metal is also the wire. The same effect as in the sphere is in the wire, the external field keeps the charges separated. You also can think, in a more abstract way, in terms of potential. Why the charges on the sphere do not get together? Because there is no potential difference between the two sides. The field of the charges on the sphere and the field of the infinite sheet compensate so that the surface of the sphere is equipotential. Connecting two points having the same potential with a wire does not result in any current flow.

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In order to sustain a current, one needs to sustain a potential difference between two parts of the conductor. If we have a closed loop, the charges eventually redistribute so as to screen the potential and the current ceases. However, if, for e.g., there is a battery in the loop, which absorbs charges on one side and injects them on the other while maintaining the potential difference, the equilibrium is never reached. One could also drive the current by changing the magnetic field through the loop, i.e., using the Faraday effect.

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