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enter image description here

Okay so in the above image the semi circular loop is rotated and a sector of it is introduced into the magnetic field.

Questions:

  1. I know the magnetic field is constant so no non conservative electric fields will be induced in the loop. Therefore, the charges must accumulate somewhere and create difference in potentials. Where will the high and low potential points be?

  2. Emf is only induced when the area of a current carrying loop increases. In the above figure the part of loop inside the current carrying wire is not a complete circuit (The two vertical lines are not wires). Why is an emf induced?

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  • $\begingroup$ You have to show some own effort first. Hint: (motion + magnetic field) - induced force on mobile charge carriers (electrons) in some wire element per unit charge is $\mathbf v \times \mathbf B$ where $\mathbf v$ is velocity of the wire element. This means there is force driving the current only in part of the circuit. Try to identify which one. $\endgroup$ Jun 6, 2021 at 23:27
  • $\begingroup$ I doubt there will be accumulation of charge, because the circuit is closed and there is nothing to prevent redistribution in the part of the circuit where no EMF is present. Maybe the assignment is wrong? $\endgroup$ Jun 6, 2021 at 23:33

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The magnetic flux through the semicircular loop is increasing. This is why an EMF is generated in the loop.

Also, this EMF is a non-conservative electric field, as $$\oint E.dl = \frac{\partial}{\partial t}\iint B.dS \neq 0$$ for the loop.

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  • $\begingroup$ there must be a conservative electric field right? Since the moving charges (Due to the electric field) will get accumulated somewhere. $\endgroup$ Dec 28, 2019 at 15:50
  • $\begingroup$ The charges don't get accumulated anywhere. There's just current flowing in the loop. $\endgroup$
    – Ishan Deo
    Dec 28, 2019 at 16:26
  • $\begingroup$ in case of motional emf the magnetic field acts as the non electrostatic force which generates an emf. Is that not the case here ? $\endgroup$ Dec 28, 2019 at 19:23
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    $\begingroup$ Motional EMF is not due to non-conservative electric field, there is no such field because the external magnetic field is not changing in time. It is due to internal forces from the moving wire acting on mobile charge carriers (electrons). This occurs as reaction to charge carriers pushing on the wire due to magnetic force. $\endgroup$ Jun 6, 2021 at 23:21

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