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Physics
Classical Physics
Electromagnetism
Surface Charge on Resistive Current Carrying Cylinder
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[QUOTE="MisterX, post: 4408571, member: 282618"] The goal is to find a reasonable solution to the surface charge density that would cause constant current through a cylinder of constant resistivity. One approach is to attempt to find a surface charge distribution on a cylinder so that the electric field on the cylinder axis is constant and non-zero. We might want to consider this for a cylinder of infinite length. If there are any solutions I would expect a family of solutions, since we could always add a uniform charge distribution and leave the E field unchanged. Essentially I think this problem is find [itex]\sigma(z)[/itex] so that [tex]\int_{-\infty}^{\infty} \frac{\mathscr{z}}{(\mathscr{z}^2 + R^2)^{3/2}}\sigma(\mathscr{z} - d) d\mathscr{z} = const \neq 0 \;\;\;\;\forall d[/tex] I don't think choosing [itex]\sigma(z) = az[/itex] results in convergence (finite E field). Perhaps a finite sized approach (maybe numerical) is warranted (maybe with charge density on the end caps). Perhaps the requirement should instead be that the E flux is constant through a cross section of the cylinder. Does anyone have any ideas? [/QUOTE]
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Physics
Classical Physics
Electromagnetism
Surface Charge on Resistive Current Carrying Cylinder
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