PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Conductors, capacitance and boundary-value electrostatics
Electricity, Magnetism and Electromagnetism, Ch Conductors, screening and capacitance
Problem
Two flat parallel conducting plates, each of area A=0.040m2, face each other across a vacuum gap d=0.20mm. The gap is tiny compared with the plate dimensions, so the field between the plates may be taken as uniform and edge effects ignored. The plates are connected to an ideal source of 60V and equilibrium is reached.
((a)) Find the capacitance and the magnitude of the charge on each plate.
((b)) Find the stored energy from 21CV2, and verify it by multiplying the field energy density 21ε0E2 by the volume of the gap.
((c)) Find the magnitude of the force that one plate exerts on the other.
((d)) A thin uncharged metal foil of the same area, of negligible thickness, is now slid into the middle of the gap parallel to the plates, touching neither plate. Give the magnitude of the induced surface charge density on each face of the foil, and say which face carries the negative charge.
((e)) Instead, a second identical capacitor (same A, same empty gap d) is connected in series with the first across the same 60V source. Find the capacitance of the series pair and the potential difference across each capacitor.