The spherical metal dome of a demonstration generator has radius and carries a charge…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential · Conductors, capacitance and boundary-value electrostatics
Electricity, Magnetism and Electromagnetism, Ch Conductors, screening and capacitance
Problem
The spherical metal dome of a demonstration generator has radius R=25cm and carries a charge Q=1.5μC in electrostatic equilibrium. The dome is far from all other conductors, so treat it as an isolated sphere in vacuum, and take V=0 at infinity.
((a)) Find the capacitance of the dome.
((b)) Find its potential.
((c)) Find the stored energy from Q2/2C, and then confirm the same number by integrating the field energy density 21ε0E2 over all the space outside the dome, using the field given by Gauss's law.