Question

An isolated conducting sphere with radius \(R=6.85\text{cm}\) has charge \(Q=1.25nC\)

a) how much potential energy is stored in the electric field of this charged conductor?

b)what is the energy density at the surface of the sphere?

c)what is the radius \(R_0\) of an imaginary spherical surface such that half of the stored potential energy lies within it?

Answer 1

my attempts:
a)\[U=\frac{Q^2}{2C}=\frac{Q^2}{8\pi\epsilon_0R}\]b)\[u=\frac{1}{2}\epsilon_0E^2\]\[u=\frac{1}{2}\epsilon_0\left(\frac{1}{4\pi\epsilon_0}\frac{Q}{R^2}\right)^2\]\[u=\frac{Q^2}{32\pi^2\epsilon_0R^4}\]
c) unsure!