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From the Biot-Savart law we se that a moving charge creates a magnetic field which, in turn, can exert a force on electric charges, thus, do the charges on, let's say, a wire, exert a force not on themselves but on its neighbouring charges?

More over, and on this I'm a little rusty, does a closed current carrying loop, be it a square, circle, pentagon, whatever, imply a null total magnetic force, if the loop is isolated from any other magnetic field and can only interact with the one created by the current that goes through it?

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Yes, the pieces of the circuit affect the other pieces of circuit via magnetic force and this is known as the Ampère force.

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  • $\begingroup$ Yes, but the ampere force is usually described for separate wires, what about charges on the same wire? Does the same apply? $\endgroup$ – Bidon May 29 '18 at 12:19
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    $\begingroup$ The same is applicable. It is known also that the force is repulsive in a closed circuit - it tries to make the circuit "larger". $\endgroup$ – Vladimir Kalitvianski May 29 '18 at 12:37
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A single closed loop is an inductor, just like the traditional spiral-shaped inductor except with less inductance because it only has one loop.

If you have current flowing through a loop of real-world slightly-resistive wire isolated from the rest of the universe, the resistor's inductance will keep the current going for a short time (with exponential decay) while all of the moving electrons apply a magnetic force on each other.

However, the "total magnetic force" on a loop (including its electrons) isolated from the rest of the universe is zero because the total force on anything isolated from the rest of the universe is zero. As the electrons collectively slow down from the resistor, they'll apply a torque on the positive charges in the loop, conserving momentum, but this is not a magnetic force.

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