E. Potential Energy: Uniformly Charged Hollow Sphere and Point Charge

[Heisenberg7]

I was doing a problem with this one detail. It says that the electric potential energy of an uniformly charged hollow sphere and a point charge is (at the surface of the hollow sphere; both positive): $$U = k \frac{q_1 q_2}{r}$$ I guess this assumes that the hollow sphere is a point charge. Now my question is, does the electric potential energy depend on other physical properties of an object? Or is this like the Newton's Shell Theorem? What if the object wasn't spherical?

 

[anuttarasammyak]

I guess this assumes that the hollow sphere is a point charge.

You do not tell us what are q_1,q_2 and r so that we can follow your guess condifently.
BTW
$$U=k \sum_{i<j}\frac{q_iq_j}{r_{ij}}$$
is a fundamental rule for system of point charges whatever distributions they have.

 

[Heisenberg7]

You do not tell us what are q_1,q_2 and r so that we can follow your guess condifently.

Charge of the sphere and the point charge respectively. $r$ is the radius of the sphere. Now, in general, does it hold if $R > r$ (where $R$ represents the distance from the center)?

 

[Orodruin]

By the shell theorem, the field outside any spherically symmetric charge distribution is the same as that of a point charge with the same total charge at the center of the sphere. Yes, this is only true for spherically symmetric distributions.

 

[anuttarasammyak]

Now, in general, does it hold if R>r (where R represents the distance from the center)?

$$U(R)=k\frac{q_1q_2}{R}$$ for R > r
$$U(R)=k\frac{q_1q_2}{r}$$ for R < r