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I am trying to resolve what is wrong with this line of thinking:

If I have DC flowing through a current carrying wire (a perfect cylindrical conductor) of radius $r$ - the magnetic field inside the wire is $B_{\text{inside}}(r)= \mu_0Ir/2\pi R^2$. Why does the Lorentz force produced by this magnetic field on the moving electric charges $\vec{F}=\vec{v} \times \vec{B}$ not push the electrons towards the axis - i.e. so that the current distribution is concentrated on axis?

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The current is indeed compressed. See https://en.m.wikipedia.org/wiki/Pinch_(plasma_physics).

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  • $\begingroup$ If you don't mind me asking - how come the entire pinch is compressed in that case - rather than just the current distribution inside of the current carrying material? Should the stationary particles that make the bulk of the material not see any of the magnetic field? $\endgroup$
    – Akerai
    Feb 20 at 10:17
  • $\begingroup$ If the electrons are compressed the local current density increases. Then temperature increases, resistance increases etc. until the material melts. Moreover, if the electrons concentrate they will pull along the metallic or plasma ions by the Coulomb force. $\endgroup$
    – my2cts
    Feb 20 at 10:32

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