Question

3) In our discussion of the proton hand grenade, the electrostatic potential energy of the proton sphere was stated as: U =1/4nEo . Q^2/R. In fact, the correct expression has

a factor of 3/5 out in front on the right-hand side. (30 pts) à) Prove this factor of 3/5 by deriving U precisely. (Hint: Treat the formation of the final sphere as a series of nested infinitesimal spherical shells of charge brought in from infinite distance, like building an onion starting from its center.) b) Calculate the total energy of the electric field surrounding the sphere and compare it to the previous result for U. Briefly and cogently comment on this.

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