Work done separating charge

vaironl

1. The problem statement, all variables and given/known data

How much work is done to separate an electron from a proton by a distance of 0.1 m?

2. Relevant equations

Work = F * d

3. The attempt at a solution

I Tried finding the electric force and then plugin it into the Work formula
Therefore (-2.31*10^-26N)(0.1m)?

daveb

W = F*d assumes the force is constant along the path. In this case, the force changes as you move the charges apart.

vaironl

I still do not know how exactly would I be able to find that work formula

Alucinor

Do you know how to do integrals and do you have an equation for the force between two charges that you can look up?

vaironl

No, sorry to disappoint you and myself, but I don't have a clue about integrals.

I know that the force between to charges is Felectric = (k)(q1)(q2)/(r^2)

Alucinor

Not a problem, there are a few ways to do problems like this one.

Do you know the relationship between work done and changes in potential energy and have an equation for the electric potential?

SammyS

How close are the electron & proton to begin with ?

vaironl

I do not know any of those, I will give my book a look and come back to that. I was thinking about it rather than doing it, a teacher I know tells me if I understand the concept I should be able to conquer all questions. Sounds weird but for some reason I see it as a good statement.

The question does not give a starting position.

Alucinor

Intro physics questions are easy mathematically, it is the concept that is difficult, as well as the visualization of the problem. So your professor is pretty correct imho.

I would look up those things I recommended as that is the main way I think it could be done relatively easily without calculus.

vaironl

That was exactly what my teacher told me. Though, he told me there is no point in plugin numbers into a formula knowing they will come out right, if you don't know what is really going on (concept).

I tried thinking about this and I came up with the following solution, most likely wrong.

But an Electric field has the following formulas.

E = f(electric)/charge = N/C = V/Meter = (J/C)/Meter

Would this be correct? because I could then isolate the Joules unit

SammyS

You cannot solve this problem without know both the initial and final separation distances.

Alucinor

You can solve it with a variable in place in the starting position though, you don't need a numerical solution, just use r₁ and r₂ = r₁ + 0.1

vaironl, try thinking about this with energy considerations. Note that "electric potential" and the "potential energy" are NOT the same thing.

A very essential idea would be that the amount of work done can be equated to the change in potential energy in this example (because we're just looking at a stationary state to another stationary state, at least that is what I gather from the wording, normally we'd have to look at both the initial potential and kinetic compared to the final potential and kinetic).

Often, energy is talked about in terms of "this is the object's capacity to do work". So you see that something must have work done on it (either positive or negative) in order to change its energy. When you have an electron sitting in a proton's E-field, it has a certain amount of potential energy due to the coulomb force. This force is conservative (very important), so we can define a potential energy for the electron (this is something that I would hope you can find in your text book). When we move the electron a radial distance away from the proton (must be radial because the system is spherically symmetric) we do work on the electron, which should result in a change in the electrons potential energy.

You might find poking around this site useful: http://hyperphysics.phy-astr.gsu.edu...volcon.html#c1
The left side of that diagram should be where you're clicking (you can ignore the "Charge" one)