I am currently working through my Nuclear Physics question sheet, and one
part of the course has me stuck. Its just a small part, but how do you
show that the potential energy due to electrostatic forces of a uniformly
charge sphere of total charge Q and radius R is
Where e is epsillon nought.
I looked in the textbook "Modern Physics" and it just says that a simple
proof can show this, albeit in a slightly rejigged way with a factor of 3
fifths at the start.
Dave Hughes <firstname.lastname@example.org> wrote in
Recognize that if you have a uniformly charged sphere of total charge Q,
radius r, and charge density p, and it has a potential energy X, then the
change in X from adding a thin shell of thickness dr is:
dX = 4*pi*r^2*p*(dr)*Q/(4*pi*e*r).
Then integrate from X=0 to X=R, using Q(r)=(4/3)*pi*r^3*p .
Eliminate p from the final answer by substituting Q(R).