Im not necessarily talking about emf (and also not considering rotation) , but rather the potential difference created due the induced electric field to balance the lorentz force on the electron. For example if the disk is moving toward the right and the magnetic field is into the screen then the lorentz force is acting on an electron downwards pushing it down. now due to the excess of electrons downwards an electric field is created top to bottom which increases until the lorentz force is equal to the force due to the electric field on the electron, resulting in an electrostatic condition. So my question is does this actually happen? if not why dosent it happen? Im a bit bothered by this because according to faradays law there should be no emf induced in the disk but according my reasoning there should be a potential difference. Is there a difference between emf and potential difference?
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Yes, there will be potential difference, due to charge separation that happens due to motional emf - emf due to motion of conductor in magnetic field. There is no induced electric field, only electrostatic field, and motional emf (due to external magnetic field). If the motion of the whole conductor is uniform, charge redistributes in such a way that its electrostatic field cancels the motional emf intensity $\mathbf v\times \mathbf B$ everywhere, so no current flows in the frame of the conductor.
answered Sep 2, 2023 at 16:02
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$\begingroup$ Thank you for answering! but can we actually refer to this as motional emf? As this is a closed surface and for e = ( V x B ).dl , im not sure if dl is even defined $\endgroup$ Commented Sep 2, 2023 at 17:31
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$\begingroup$ EMF is always defined for some path, closed or open. So choose a path $\gamma$ in space, and motional EMF for that path is $\int_\gamma \mathbf v\times \mathbf B \cdot d\mathbf s$. $\endgroup$ Commented Sep 2, 2023 at 18:38