Posted by jude on Sunday, April 4, 2010 at 5:59pm.
U = - (1/4 pi eo)e^2 / r
Negative because 0 at infinity and drops as it gets closer
F = (1/4 pi eo) e^2/r^2 = m a = m v^2 /r
m v^2 = (1/4 pi eo) e^2/r
so
KE = (1/2) m v^2 = (1/2) (-U)
the KE is half the magnitude of the potential energy at every radius.
Total energy = (1/2)(1/4 pi eo)e^2/r - (1/4pi eo) e^2/r
= -(1/2) (1/4 pi eo) e^2/r
Energy at R =-(1/2) (1/4 pi eo) e^2/R
Energy at 2R = -(1/2)(1/4 pi eo) e^2/2R
Because of - sign, the total energy is higher at the bigger radius by a factor of 2
The potential energy goes up by more than the kinetic energy goes down.
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