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I was studying the chapter electric current and came up with a doubt in my mind . Basically when we pass electric field through a conductor then as the dielectric strength of a conductor is very high so it will be as following-

  1. The electrons inside the conductor will move in presence of the field untill the density of the opposite charges becomes enough to oppose the external field provided by us .

    1. So net electric field in a conductor is always zero

Then I thought that it may possible that when we connect a battery in a circuit then due to the electric field produced by the battery the electrons inside the conductors of the circuit starts flowing And instead of accumulating at one place as that of the previous one it goes on moving inside the loop so here it's seen that inside the conductor the electric field is not zero . That when a conductor is bend in the form of a loop and used in a circuit with a battery then the electric inside it is non zero. Then why does we assign the same potential between any two points inside a conductor in a circuit though we know that in any electric field potential is different at different points

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If you make the assumption that the conductor (connecting wire?) has no (very little) resistance then the potential difference across the conductor is zero ( very small) as there is no (very little) opposition to the flow of charges.

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The problem you face is that there are no "ideal" circuit components. As a result, any wire always has some resistance. Also, any real battery also has some internal resistance.

If you add those "parasitic" resistances to your ideal circuit, things suddenly start to make more sense. If you connect the terminals of the battery with a wire, the current will be limited by the resistance of the wire and the battery, which are in series. This total resistance will limit the current. The voltage along the wire will vary, using Ohm's law of V=IR, so that there will be different voltages at different points along the wire. And, of course, for the same reason, the EMF will vary inside the battery. In other words, there is always an EMF inside a real wire.

We can normally ignore this because the resistances of the battery and wire are usually negligible compared to the other components in the circuit. It's only when they are not negligible that we have to seriously include them in our calculations.

This problem goes beyond simple resistance. When you are dealing with varying currents (or AC) you need to allow for the fact that even a straight wire has some inductance, and there is always some capacitance between different points of a circuit. Even just connecting a battery via a wire means that the current will suddenly increase at the moment of connection, and capacitive and inductive effects happen at that time.

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