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?