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Let's say if I have a circuit like shown in the picture below. The green wire is not rigidly connected to the black wires, but this green wire can move while maintaining the electrical connection. Like a connection between moving tram and wires or the “third rail”.

In the beginning, nothing is moving and my Ammeter shows 1 Amper current. Now green wire starts moving in the same direction as electrons inside the wire (let say everything is copper wires). Black wires and Ammeter is not moving.

What will my Ammeter show and why? The same 1 Amper or different? and if different is there a way to calculate?

From first glance, the electrons inside copper green wire are going faster in relation to Ammeter and Ammeter can show higher current. Based on this Wikipedia article real speed of electrons is very small (meter per hour), then even small movement should increase the current.

And if everything is moving directly with the constant speed, then according to relativity everything will be the same and current as well. The only question is what if Ammeter is not moving, but the green wire is moving.

I am considering for now only an ideal theoretical system, vacuum, no external magnetic field, no friction in the connection between black and green wires, the connection is ideal without any losses, etc.

enter image description here

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Current would be 1 ampere only. Since you are moving both electrons and protons of the wire by moving the wire, you are actually not doing anything. Effectively you still have electrons moving with drift velocity in the same direction as initial.

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  • $\begingroup$ I think you are right. I need to think about accelerated wire, not moving with constant speed :) $\endgroup$
    – Zlelik
    Mar 10 '20 at 12:33
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Note that in the configuration drawn the ammeter is not measuring the current through the green wire but rather the current through the black wire. The “background” current through the green wire is not relevant except insofar as it affects the resistance of the green wire (e.g. by heating it up).

Note that circuit theory is a non-relativistic theory, so you cannot simply apply the principle of relativity here. However, assuming that the green wire is ideal (no resistance) and assuming $v<<c$ so that relativistic deviations from circuit theory are negligible then the current will be the same 1 A and will still be driven by the voltage source on the left and the resistor on the right.

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