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

• B
• Heisenberg7
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?

Heisenberg7 said:
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.

Last edited:
anuttarasammyak said:
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)?

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.

Heisenberg7
Heisenberg7 said:
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

Heisenberg7

• Electromagnetism
Replies
11
Views
1K
• Introductory Physics Homework Help
Replies
23
Views
927
• Electromagnetism
Replies
26
Views
2K
• Electromagnetism
Replies
11
Views
2K
• Electromagnetism
Replies
4
Views
769
• Electromagnetism
Replies
7
Views
1K
• Electromagnetism
Replies
4
Views
1K
• Electromagnetism
Replies
3
Views
1K
• Electromagnetism
Replies
2
Views
914
• Classical Physics
Replies
16
Views
700