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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?

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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.

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  • $\begingroup$ @KavleenMarwah If you found this to be a good answer to your question, you can indicate this by accepting it. $\endgroup$ – Nat May 31 '18 at 16:59
  • $\begingroup$ @Nat I am so sorry! At it rn! $\endgroup$ – KavleenMarwah May 31 '18 at 17:09
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I believe the reasoning here is slighty different. The magnetic field created by one part of the wire is perpendicular to the current and for a force to act you again need a magnetic field perpendicular to the current, which you have for a non bend straight wire. However without a bend in the wire you do have a cylindrical symmetry in the problem.

The electric current can not produce a magnetic field on the axis it flows because in what direction is this field supposed to be. It could only be along the line of the current, which as you pointed out wouldnt have any effect. You don't change the configuration if you rotate the wire. So I believe you are correct in that there is no way for one part of a straight wire to exert a force on another part.

I just realised maybe that was your reasoning anyway?

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