Expressing the interaction energy between two spheres?

In summary, the interaction energy between two spheres is dependent on their distance and the properties of their surfaces. When the spheres are close together, the energy is attractive and decreases as the distance between them increases. However, if the spheres have opposite charges or polarities, the energy can become repulsive at certain distances. Additionally, the roughness or smoothness of the spheres' surfaces can affect the strength of their interaction energy. This interaction energy is important in understanding and predicting the behavior of particles in various systems, such as colloidal suspensions and molecular interactions.
  • #1
Spiral1183
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Homework Statement


Two identical spheres with radius R have uniform charge Q throughout their volume and separated d>2R apart


Homework Equations


https://www.physicsforums.com/attachment.php?attachmentid=63061&d=1382054852 is the general potential energy equation

attachment.gif
this should be my total charge inside a sphere?

attachment.gif
This is the equation for the interaction energy

The Attempt at a Solution


I found the total charge of the sphere (2nd Eqn.) and I believe that to find the interaction energy, I should treat that as [itex]\Phi[/itex]1 and then use the charge from sphere 2?
 

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  • #2
My issue is that I don't understand what the potential equation is asking for, as I am not sure how to plug in the two charges and the distance (d) into this equation. Any help would be great!
 

1. How do you calculate the interaction energy between two spheres?

The interaction energy between two spheres can be calculated using the formula E = 2πεa1a2/R, where ε is the permittivity of the medium between the spheres, a1 and a2 are the radii of the spheres, and R is the distance between their centers.

2. What factors affect the interaction energy between two spheres?

The interaction energy between two spheres is affected by the distance between the spheres, the size of the spheres, and the dielectric constant of the medium between them. It is also influenced by any charges present on the spheres.

3. How does the interaction energy between two spheres change as the distance between them decreases?

As the distance between two spheres decreases, the interaction energy increases. This is due to the stronger attraction between the spheres as they get closer together.

4. Can the interaction energy between two spheres be negative?

Yes, the interaction energy between two spheres can be negative if the charges on the spheres are of opposite signs. In this case, the spheres will repel each other and the interaction energy will be negative.

5. How is the interaction energy between two spheres related to their surface area and charge?

The interaction energy between two spheres is directly proportional to their surface area and the product of their charges. This means that as the surface area or charge of the spheres increases, the interaction energy also increases.

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