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

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The discussion centers on the electric potential energy between a uniformly charged hollow sphere and a point charge, specifically at the surface of the sphere. It is established that the formula for electric potential energy, U = k(q1q2/r), assumes the hollow sphere behaves like a point charge due to the Shell Theorem. The conversation explores whether this relationship holds for non-spherical objects and under different conditions, emphasizing that the formula applies for spherically symmetric charge distributions. The potential energy is defined differently based on the distance from the center of the sphere, with U(R) = k(q1q2/R) for R > r and U(R) = k(q1q2/r) for R < r. The discussion concludes that the electric potential energy is contingent on the symmetry of the charge distribution.
Heisenberg7
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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?
 
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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&lt;j}\frac{q_iq_j}{r_{ij}}
is a fundamental rule for system of point charges whatever distributions they have.
 
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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.
 
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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
 
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