If a charged copper solid sphere (radius R=1mm and total uniform charge througho

Question

If a charged copper solid sphere (radius R=1mm and total uniform charge throughout Q) is allowed to disperse, this "self-energy" (energy needed to assemble this charge) will appear as kinetic energy of the individual charges. Assume the sphere is composed of copper, except that all of the positive ions have been removed, leaving only the conduction electrons. What is the amount of "self-energy", in Joules, will be converted to kinetic energy when this charge is dispersed?
The energy needed to assemble a solid sphere is U=(3*Q^2)/(20*pi*epsilon*r)
Copper has one conduction electron per atom. Its mass density is 8.96g/cm^3, and its atomic mass is 63.546g/mol
Please show all steps, thank you!

Explanation / Answer

You don't need a double or a triple with this one. Uniform volume charge density ?: k = 1 / 4p*epsilon_0 dUe = k q(r)*dq(r) / r dUe = k (4/3)pr^3?*4pr^2?*dr / r dUe = k (16/3) p^2 ?^2 r^4 dr Ue = k (16/3) p^2 ?^2 ? r^4 dr [0,r] Ue = k (16/15) p^2 ?^2 r^5 *(r/r) ==>q=(4/3)pr^3*? Ue = (3/5) k q^2 / r = (3/20) q^2 / (p*epsilon_0*r)

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