# Potential difference between two points problem

## Homework Statement

Given a point charge of 500pC at the origin, find the potential difference between points a and b at distances 5m and 15m respectively along the x-axis.

## Homework Equations

Coulomb's law, I think?

## The Attempt at a Solution

The reason I thought coulombs law was relevant was because it was mentioned in the first part of the equation. I tried to apply Coulomb's law, but got nowhere, as I don't have a charge for a and b, and also, I think that would ignore the charge at the origin, so it was probably the wrong way to go about it. To be honest, it just doesn't seem to me like there is enough information given to do anything with it, really.

Have you learned anything called as electrostatic potential??
If not, read some book and grab an idea of it. It will help you to understand the problem!

Redbelly98
Staff Emeritus
Homework Helper
Yes, please do look in your physics textbook, in the section or chapter on electric potential.

You are looking for the potential (or voltage) of a point charge -- there should be a formula for this.

I looked, but couldn't find anything really. Wouldn't I need to know the charge at a and b to do anything?

jhae2.718
Gold Member
I looked, but couldn't find anything really. Wouldn't I need to know the charge at a and b to do anything?

It's a point charge, so no.

Change in electric potential is defined as $$[V(\mathbf{r_2})-V(\mathbf{r_1})] = -\int_{\mathbf{r_1}}^{\mathbf{r_2}} \!\!\! \mathbf{E} \cdot d\mathbf{r}$$

What is the electric field for a point charge?

r1 and r2 are distances from the origin, right? But what is V? also, is E the electric field, which is F/q? If so, I would need q, the charge at each point, wouldn't I? but you said I didn't.

I think I worked this out, would appreciate if someone could confirm my answer.

500pC = 500x10^-12 C
Potential at a point = Kₑ (q/r)
applied these and got:
Va = 9x10^-12
Vb = 3x10^-10
Potential difference between a and b = |Va - Vb|
=> 2.91x10^-10

Redbelly98
Staff Emeritus