- #1
fluidistic
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Homework Statement
Same problem as in https://www.physicsforums.com/showthread.php?t=589704 but instead of a spherical shape, consider an infinite line of constant charge density [itex]\lambda _0[/itex].
Homework Equations
Given in the link.
The Attempt at a Solution
I assume Phi will be the same along any parallel line to the charge distribution. So I can calculate [itex]\Phi (y)[/itex] in an x-y plane where x is the line direction and y=0 is where the line is.
I get that [itex]|\vec x - \vec x'|=\sqrt {x^2+y^2}[/itex] so that [itex]\Phi (y)=\int _{-\infty }^{\infty } \frac{\lambda _0 dx}{\sqrt {y^2+x^2}}=\lambda _0 \ln ( \sqrt {y^2+x^2 } ) \big | _{-\infty}^{\infty}[/itex] but this diverge.
By intuition I know that the equipotentials must be parallel to the charge distribution but here I get that the potential is infinite everywhere.
I don't know what's going on.