# Potentials of charge distribution

1. Oct 8, 2005

### don23

The question says that charges are distributed with uniform charge lambda along a semicircle of radius R, centered at the origin of a coordinate system. What is the potential at the origin?

I am not sure how to approach this one. Can anyone help me set this up and solve it? Thanks!

2. Oct 8, 2005

### Pyrrhus

Did you notice all dQ are at the same distance from O?

3. Oct 8, 2005

### mezarashi

For questions in electrostatics, the general strategy is to look for symmetry. Once you have established some sort of symmetry, use it to your advantage. You know the differential form of the potential function

$$V = \int \frac{k dq}{r}$$
However from your geometric analysis, you only have r in your equation with no dr variable of integration. Instead you have a dq. You can relate the charge density to the length usually through something like

q=$$\rho$$r where $$\rho$$ is the charge density, then
dq=$$\rho$$dr

Substituting this in, you will finally be able to solve the integral and get your answer. Give it a try.

Last edited: Oct 8, 2005