# How can I derive the equation for electric potential at a distance r from a charge Q?

1. Aug 29, 2009

### FelixISF

1. The problem statement, all variables and given/known data
Find the electric potential a distance of .5 x 10^-10 m from the proton of a hydrogen atom

2. Relevant equations
V= kQ/r

3. The attempt at a solution
I know how to answer the question, because I know which equation to use. What I do not understand is, where the equation comes from ?
Could somebody bullet point the derivation of the equation (algebra, not calculus please )

Regards and Thanks!

2. Aug 30, 2009

### tiny-tim

Hi FelixISF!
It comes from the field (the force), which in this case is a Coulomb's law field.

The field has to be the gradient of the potential.

The field is -kQ/r2 in the r-direction, so the potential has to be kQ/r (plus a constant).

(That's calculus, of course … I don't understand what you mean by an algebra derivation )

3. Aug 30, 2009

### FelixISF

Re: How can I derive the equation for electric potential at a distance r from a charg

I don't see how you go from -kQ/r^2 to kQ/r... Apart from the mathematical relation ship of the field being the gradient of the potential, I don't get the intuition behind it.
so field = -kQ/r^2 and potential = kQ/r
Now, there must be a relation between potential and field with which you can transform the field equation to the potential equation.. Do you understand what I am asking for?

4. Aug 30, 2009

### espen180

Re: How can I derive the equation for electric potential at a distance r from a charg

Use the equation $$V=\int_{\infty}^{r}\vec{E}\cdot \vec{dl}$$ where V is the electric potential. In the case of a point charge you can substitute $$\vec{dl}=dr$$ and $$\vec{E}=E$$, so your integral becomes $$V=\int_{\infty}^r E \; dr$$.

5. Aug 30, 2009

### tiny-tim

In other words, potential energy is another name for work done (by a conservative force),

so electric potential difference = PE difference per charge = work done per charge = force times distance per charge = kQ/r2 times ∆r

6. Aug 30, 2009

### FelixISF

Re: How can I derive the equation for electric potential at a distance r from a charg

thanks, that made it clear for me!