# Find the Potential as a function of position

1. Jan 31, 2007

### prace

1. The problem statement, all variables and given/known data
A rod of length L carries a charge Q uniformly distributed along its length. The rod lies along the y-axis with one end at the origin. Find the potential as a function of position along the x-axis

2. Relevant equations
$$dV=\vec{E}\cdotp d\vec{l}$$

$$V=\frac{kq}{r}$$

3. The attempt at a solution

I think I am to use the first equation posted, but I am not sure how to relate it to the x-axis, if the rod lies along the y-axis. Also, what is the displacement here? I am assuming it is just dy?

2. Jan 31, 2007

### Andrew Mason

You have to integrate along the rod from y = 0 to +L.

$$V(x) = \int_{0}^{L} \frac{k}{r}dq$$

Work out the expression for dq in terms of dy. Work out the expression for r in terms of x and y (think: Pythagoras).

AM

Last edited: Jan 31, 2007