1. Spherical capacitor [4 points (hand-in)] Consider a metal ball of radius R and with charge Q, surrounded by a thick m

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1 Spherical Capacitor 4 Points Hand In Consider A Metal Ball Of Radius R And With Charge Q Surrounded By A Thick M 1 (209.97 KiB) Viewed 14 times

please solve those questions a to d step by step and if you are handwriting then please write the letters clearly. Thank you so much.
1. Spherical capacitor [4 points (hand-in)] Consider a metal ball of radius R and with charge Q, surrounded by a thick metal shell with inner radius a and outer radius b. The shell carries no charge. a) Derive the electric field E(F) and give the surface charge den- sity o of the conductors at R, a and b. Make a sketch of the sphere showing the location of the charges. b) Derive the potential o(7), setting (oo) = 0 as a boundary condition. c) Compute the capacitance C₁ between the ball and the inner side of the shell and C₂ between the outer side of the shell and infinity. d) Compute the energy of the electrostatic field. Use the following facts: - Charges cannot exist inside conductors but always accumulate on their surface. C The electric field outside any charge distribution is known in the spherically symmetric case (by application of Gauß theorem). - The surface charge density is proportional to the electric field at the surface.