# What is the electrostatic potential energy of a sphere?

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1. Oct 19, 2016

### Jhoan Steven

Hello! I'm Steven, and I'm currently working on the following problem:
The earth can be seen as a conducting sphere with an electric field: E= -(150V/m)r (on its surface)
and where r is the unit vector . The earth has a radius 6371 km.

So, I am asked to calculate the electrostatic potential energy of the sphere, and then, as the Gravitational potential energy is very similar to the electrostatic potential energy, calculate this one as well. After the calculation I'm told to discuss in what way these forces affect the earth's structure.

This is what I have tried:

I know that the work is defined as ∫F.Dr
so the definition of electric force is: qE.
integrating I will have U=qE/r
the electric field is given but I don't know what to do with that q there.

I know the gravitational potential energy is defined as U=mgh
so here should I replace the m with the mass of the earth and its acceleration? and h will be its radius?

The last part I think that these forces somehow act upon the earth's poles, so that's probably the reason they are a little shrunk?

Thank you, I hope you can help me out :)

2. Oct 20, 2016

### rude man

I think you mean potential, not potential energy.

In an E field, what is the (usual or standard) definition of potential?