- #1
Hydroshock
- 7
- 0
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.
"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.
V = int|kdq/r
dq = λdx
λ = Q/L
r = x0 - x
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?
Homework Statement
"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.
Homework Equations
V = int|kdq/r
dq = λdx
λ = Q/L
r = x0 - x
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?
Last edited: