# Voltage on a point charge from a stick of charge

1. Feb 26, 2013

### Colts

1. The problem statement, all variables and given/known data
In the figure the rod has a charge density of ßx, where x=0 is the left end of the rod, etc. Find the electric potential energy of the point charge q a distance a from the end of the rod and lying along the rod's axis.
http://www.usi.edu/science/physics/pickett/206/4p4f1.jpg [Broken]

2. Relevant equations
V=$\frac{q}{4\pi\epsilon r}$

3. The attempt at a solution
Since it is voltage from the whole rod it should be an integral, but where I'm not sure at is what should be on top of the fraction

The integral is from 0 to L
$\int\frac{q}{4\pi\epsilon (a+L-x)}dx$
or
$\int\frac{\beta x}{4\pi\epsilon (a+L-x)}dx$

Last edited by a moderator: May 6, 2017
2. Feb 26, 2013

### haruspex

To calculate the voltage where the point charge is, the point charge itself is irrelevant. You want the voltage generated by the charge distribution on the rod, so it's the second integral.