Potential/inverse nth power law

[granpa]

Homework Statement

is the potential in the center of a solid 3d sphere having uniform mass density and a total mass of m (which is constant), which is gravitating according to an inverse 10th power law, inversly proportional to the square of its radius? this isn't really homework but I figured people would think it was anyway. (this concerns nuclear forces and potentials). the number 10 has no special significance.

Homework Equations

potential at point x = energy released in moving from infinty to point x.
energy=force * distance

The Attempt at a Solution

the calculus is far beyond me but intuition and symmetry tell me that it must be.

obviously the field is negligible everywhere except very close to the surface of the sphere. if the radius is cut in half then the density would be 8 times as great.
so we can think of this as making the field everywhere 8 times as great but halving the distances involved so the potential would be 8/2 times as great.

 

[Dick]

That's is so wrong headed in all respects. You said 'uniform density', how does cutting the radius in half increase the density by 8? If you are trying to apply Gauss' law, it only applies to inverse square fields in 3 dimensions. Now it's your turn. Tell me what else is wrong? Why don't you just use calculus?

 

[granpa]

radius is the variable. mass is constant.I want to know the potential as a function of radius.
half the radius=1/8th the volume. hence 8 times the density. uniform density means that the mass is distributed uniformly throughout the 3 dimensional interior of the sphere.

though I had no thought of using gauss's law nevertheless it is a fact that gauss' law applies to inverse 10th power law in 11 dimensions. you can think of the sphere as being a flat 11 dimensional object. you should be able to see immediatly that (within the 3 dimensions containing the sphere) the field is negligible everywhere except very near the surface of the sphere.

 

[granpa]

anybody?