Lorentz force $\vec F$ for an external magnetic field $\vec B$ is $$ \vec F = q \vec v \times \vec B $$ and the magnitude of this force is $ F = (qv \times B) \sin \theta $.
According to this equations Lorentz force is perpendicular to both the magnetic field and the direction of the movement of the electrons. So the only possible way for a current carrying wire to exert a force on elements of the same wire is to bend one portion of the wire to some angle $ \theta$ with the other wire. Am I right? Is there any other way too?
Best Answer
Current in a wire certainly does exert internal forces. The wire is slightly compressed (to a smaller diameter) due to that internal force. This is an important effect in high-current discharges, and is called 'Z-pinch'. It presumably is also dominant in the "exploding wires" effect, and in the lightning-strike mineral, "fulgurite", which adopts a long thin shape.
A curved wire, of course, generates a variety of forces; a solenoid, for example, where current is circumferential in a cylinder, will both expand in radius and decrease in length when a high current is applied. Very high field magnets are of odd design because such forces can exceed the material strength of the wire (or machined alloy), e.g. a Bitter magnet.