Alright, well I wanted to see what help I could get here, my professor had assigned this problem and when someone in class asked a question, he started doing it on the board and after using ~15min of class time decided there was an issue with the problem. The problem got progressively harder (which leads me to believe he must have made a mistake) and he ended up deciding we don't have to do it, but i'm interested in getting it done anyway.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

"A rod of length L has a total charge Q uniformly distributed alone its length. The rod lies along the x axis with its center at the origin. (a) What is the electric potential as a function of position along the x axis for x > L/2? (b) Show that for x >> L/2, your result reduces to that due to a point charge Q.

2. Relevant equations

V = int|kdq/r

dq = λdx

λ = Q/L

r = x0 - x

3. The attempt at a solution

Well what the problem was when we got to (b). Which after setting up the equation we ended up with

[tex] k\lambda\int_{-L/2}^{L/2}\frac {dx} {x_0-x}) [/tex]

where after substitution we get

[tex] k\lambda\int_{-L/2}^{L/2}ln(x_0-x) [/tex]

but since there's units (meters) for x, it can't be run through a transcendental function, then I got lost here, but with more substitution we ended up with

[tex] V = k\lambdaln\frac {x_0-1/2} {x_0+1/2} [/tex]

then when the problem got going, it expanded and expanded and didn't get any simplification going, which is odd for a textbook question. I guess it's more of needing a check with the math work done in the problem?

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# Homework Help: Uniform charge across a rod, Professor couldn't answer

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