# How to find electrostatic interaction energy?

1. Jan 13, 2016

### gracy

How to find electrostatic interaction energy between two uniformly charged conducting spheres /uniformly charged non conducting spheres or between a charge and uniformly charged spherical shell I mean what is general method of finding electrostatic energy in a given system.I don't have any specific problem based on it therefore I am not posting it in homework section.

2. Jan 13, 2016

### Staff: Mentor

Your best approach will be Jefimenko's equations.

3. Jan 13, 2016

### cnh1995

Force between the charges=kq1q2/r2.
Interaction energy=force between charges*distance between them.
E=kq1q2/r.

4. Jan 13, 2016

### jbriggs444

It makes little sense to say that a sphere is both uniformly charged and conducting. If it is conducting, it will not remain uniformly charged. So if it is uniformly charged, it must not be conducting.

By "interaction energy", I assume that you want to know the electrostatic potential energy that the assembly of charged objects has when assembled as compared to the electrostatic potential energy that they would have if the objects were all infinitely far apart. In particular, you want to ignore the self-energy of each charged sphere or shell.

You appear to be interested in the simplest case -- two objects only and are probably interested in the case where the objects do not overlap/contain each other.

Why would you not use the formula for the potential energy of two point charges in that case?

5. Jan 13, 2016

### gracy

I meant surface charge distribution is uniform.Surface of a conducting sphere is uniformly charged.

6. Jan 13, 2016

### jbriggs444

So we will pretend for the sake of this exercise that the surface charge distribution remains approximately uniform even in the face of an externally imposed field. That's fine. Though it might have been simpler to skip the "conducting" adjective and go with "uniformly charged".

7. Jan 13, 2016

### cnh1995

8. Jan 13, 2016

### Staff: Mentor

Gracy, if you allow for charge movement due to interaction of the fields of the spheres (i.e. if you assume conducting spheres) then the problem is not at all trivial. Relative sphere sizes and separations can have interesting effects on the behavior (where "interesting" can mean non-intuitive or complicated).

Remember how a charged object can be attracted to an uncharged (neutral) conductive object due to induced charges? Well induced charges can also affect the interaction of charged objects like conducting spheres and produce some somewhat counter-intuitive results (like similarly charged spheres actually attracting each other under certain circumstances).

For example, have a look here: Electrostatics of Two Charged Conducting Spheres

9. Jan 13, 2016

### gracy

How can I apply it for two spheres and for one sphere and charge q?By treating two spheres as if whole charge of these spheres is concentrated in centre and then will multiply it by distance between the centers of the two spheres.This was for two spheres case for one sphere and one charge system we will assume the same for sphere whole charge of sphere is kept on centre and then for distance we will take distance between that charge and centre of the sphere.
Right?

10. Jan 13, 2016

### cnh1995

I don't follow.. If there is only one charge present, the sphere will have self energy only. For interaction energy, there must be more then one charges present.

11. Jan 13, 2016

### gracy

one sphere along with charge q will form a system , charge q isn't alone!

12. Jan 13, 2016

### cnh1995

Yes. I believe there will only be self energy since there is only one charge q present on the sphere.

13. Jan 13, 2016

### gracy

no sphere is with it's charge say Q which is uniformly distributed on it's surface and there is also charge q

14. Jan 13, 2016

### cnh1995

At the center?

15. Jan 13, 2016

### gracy

it can be anywhere

16. Jan 13, 2016

### cnh1995

Ok.

Right.

17. Jan 13, 2016

### gracy

18. Jan 13, 2016

### jbriggs444

When you treat a charged sphere as if the charge were concentrated in its center, treat the charged sphere as if the charge were concentrated at its center. Do not complicate things. Yes, the potential is still given by $k\frac{q_1 q_2}{r}$ where r is the distance between the centers.

The caveats is that this only applies as long as the charge on the sphere(s) is uniform (or at least spherically symmetric) and that the two objects do not overlap. If your charge $q_1$ is in the interior of a sphere with charge $q_2$ then the above formula will not apply.

[All of which was already said in post #4 above]

19. Jan 13, 2016

### cnh1995

I believe that's right too.

20. Jan 13, 2016

### nasu

As long as the charge distribution is uniform on the spheres (or just have spherical symmetry, you can treat them as point charges in the center, when dealing with fields outside the spheres.
The condition in bold letters will not apply in most cases with conductive spheres in external field of other spheres or point charges.