In my AP physics guide the graph for electric potential (for a radial field, i.e. point charge) and gravitational potential (for radial field, i.e. point mass) slightly differ from each other and I want to know the "math" behind this.
The one given for gravitational potential:
Ones for electric potential:
I am not worried about there being two graphs for electric potential because I know this is because electric potential is positive or negative depending on the charge whose electric field is being described. However, I noticed that the gravitational field graph only starts at $R_E$, which is defined in the book as being the radius of the mass we are describing. On the other hand, there is no corresponding $R_E$ for the electric potential graphs. Does that mean that electric potential is also defined inside a charge as well as above its surface? (I assume gravitational potential is not defined inside a mass because the given graph for gravitational potential stops at $R_E$)
Best Answer
The difference probably is that the graph for the gravitational potential is the one for a spherical mass distribution (or a sphere with a certain mass if you wish) and the electric one is given for a point charge. You could also draw the gravitational potential for a point mass, then it would look equivalent to your electrical potential, or the other way round.
In both cases you can calculate the electric/gravitational potential inside a charge/matter distribution. Note however, that it would look different than the one you presented here. So what you can not do is simply extend the same graph for the inside of your distribution.