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The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point.

In a DC/AC electric circuit, we say that an electric field is set up between terminal of source and so charges move between terminals.

Once charges start moving,can't we anymore say that force that acts on the charge to move it in between terminals is due to Electric field since it is defined for Charges at rest?

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  • $\begingroup$ Charges don't move because of the existence of electric field, they move due to difference in electric potential between two points. If the electric field is uniform, the charge will stay. If there is a change in electric field, then charge will move i.e. you will see current. $\endgroup$ – LostCause Jul 11 '19 at 15:35
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    $\begingroup$ @LostCause, how do you produce an difference in electric potential without the existence of electric field? The definition of the electrostatic potential difference is a path integral over the field. $\endgroup$ – The Photon Jul 11 '19 at 16:00
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    $\begingroup$ @LostCause That is like saying "Object's don't fall because of a gravitational field. They fall because of the difference in gravitational potential energy". Plus... charges will definitely move (accelerate) in a uniform electric field, just like how objects fall in a uniform gravitational field. $\endgroup$ – Aaron Stevens Jul 11 '19 at 16:17
  • $\begingroup$ @ThePhoton when you solve that integral, you assume that electrostatic potential at infinity is 0. The reason that assumption works well because we don't care about the true value, we only care about the difference. $\endgroup$ – LostCause Jul 11 '19 at 17:05
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    $\begingroup$ @LostCause Positive charges accelerate in the direction of any electric field if no other forces are acting on them. $\endgroup$ – Aaron Stevens Jul 11 '19 at 17:22
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The force on the charge due to the electric field doesn't depend on whether the charge is moving or at rest (at least so long as we can neglect relativistic effects).

The reason we might stipulate that the electric field is defined in terms of the force on a test charge at rest is not because electric field affects moving charges differently than charges at rest. It's only so that we know the force on the test charge is entirely due to the electric field, and doesn't have any contribution from whatever magnetic field might also be present at the same point.

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