# Solving potential of electron inside the nucleus

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1. Nov 6, 2016

### haseeb

1. The problem statement, all variables and given/known data
I want to derive the following equation. It is the potential energy of an electron inside a nucleus assumed to be a uniformly charged sphere of R.

2. Relevant equations

V'(r) =( -Ze2/4∏ε0R)(3/2 - (1/2)(r/R)^2)

3. The attempt at a solution
I get E = Ze2r/(4∏ε0R3)

But I am having problem in integration limits and hence going towards final required result!

Last edited by a moderator: Nov 6, 2016
2. Nov 6, 2016

### Staff: Mentor

Something went wrong with the formatting.

The electric field should be linear with the distance - right. You can check if the electric field at the border of the nucleus agrees with the electric field of a point-charge. If yes, your result is right.

3. Nov 16, 2016

### haseeb

First, Electrical field is not linearly dependent on distance! And I am not trying to find the field at the nucleus border but inside it. Can you help please to reach the desired formula?

4. Nov 16, 2016

### Staff: Mentor

Inside a homogeneously charged sphere, it is proportional to the radius, its magnitude is proportional to the distance to the center.

If your formula reproduces this relationship and agrees at the boundary, then it is right. Hence the suggestion to check if it fits at the boundary.

5. Nov 17, 2016

### haseeb

Yup! You are right... But How to drive it mathematically?

6. Nov 17, 2016

### Staff: Mentor

The shell theorem should help.