(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The figure shows a thin rod of length L and charge Q. It lies directly along the x axis with its center at the origin. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod. (Give your answer in terms of x, L, Q and appropriate constants.)

2. Relevant equations

[tex]V=Q/(4\pi\epsilon_{0}x)[/tex]

[tex]\lambda=Q/L[/tex]

3. The attempt at a solution

I know that I have to integrate each infinitesimal potential, but I am not sure what bounds to integrate over? Here is what I have done so far:

[tex]dQ=\lambda*dx[/tex]

[tex]dV=dQ/(4\pi\epsilon_{0}x)=\lambda*dx/(4\pi\epsilon_{0}x)[/tex]

Now, when both sides are integrated the result is:

[tex]V=\lambda/(4\pi\epsilon_{0})\int(1/x)dx[/tex]

The integral becomes a natural log. I have tried with several combinations of lower boundaries (0, -L/2, +L/2) and upper boundaries (L/2, x) but none of my results are correct (I get instant feedback on whether my answer is correct).

Thanks!

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# Electric Potential of a Finite Rod

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