Calculating Electric Potential of a Proton in Hydrogen Atom

[FelixISF]

Homework Statement

Find the electric potential a distance of .5 x 10^-10 m from the proton of a hydrogen atom

Homework Equations

V= kQ/r

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!

 

[tiny-tim]

Hi FelixISF!

V= kQ/r
…
What I do not understand is, where the equation comes from ?
Could somebody bullet point the derivation of the equation (algebra, not calculus please )

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 )

 

[FelixISF]

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?

 

[espen180]

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 $$V=\int_{\infty}^r E \; dr$$.

 

[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

 

[FelixISF]

thanks, that made it clear for me!