Mass, charge etc. at a single point

[ForMyThunder]

I have come across a question. When is it possible to model a given force as being directed to a single point? I know that if you are outside of the Earth, you can say that the mass of the Earth is concentrated at its center. But if you had, say, three equidistant points of charge, you can model them as a single point (I tried doing this while calculating the work it would take to move an electron from a finite distance to an infinite distance and the answer I got was wrong). What is the general principle as to doint this?

I figure it has something to do with the assumption that the Earth is homogeneous.

 

[Feldoh]

You can't model charge in the same way because charge can have different signs. For instance if we have proton and an electron and we look at it far away you might be tempted to say that the electric field is zero because the charges cancel out, however there is a field and we can calculate it.

There's a general way to account for charges at large distances it's called a multipole expansion.

EDIT: Here's a good introduction -- http://www.pa.msu.edu/~duxbury/courses/phy481/Fall2009/Lecture14.pdf

 

[Bill_K]

I figure it has something to do with the assumption that the Earth is homogeneous.

It does not have to be homogeneous, but it has to be spherically symmetric. It's an important theorem in Newtonian mechanics that the external gravitational field of a spherically symmetric mass distribution is the same as that of a point mass located at its center. A similar theorem holds also for spherically symmetric charge distributions.