- Consider A Metal Ball Of Radius R And With Charge Q Surrounded By A Thick Metal Shell With Inner Radius A And Outer Rad 1 (177.16 KiB) Viewed 16 times
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 Ē(~) 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. R b) Derive the potential o(r), 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. - 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. Q a