This problem extends the reasoning of Section 26.4, Problem 26.37, Example 30.6, and Section 32.3.
(a) Consider a capacitor with vacuum between its large, closely spaced, and oppositely charged parallel plates. Show that the force on one plate can be accounted for by thinking of the electric field between the plates as exerting a “negative pressure” equal to the energy density of the electric field.
(b) Consider two infinite plane sheets carrying electric currents in opposite directions with equal linear current densities Js. Calculate the force per area acting on one sheet due to the magnetic field created by the other sheet.
(c) Calculate the net magnetic field between the sheets and the field outside of the volume between them.
(d) Calculate the energy density in the magnetic field between the sheets.
(e) Show that the force on one sheet can be accounted for by thinking of the magnetic field between the sheets as exerting a positive pressure equal to its energy density. This result for magnetic pressure applies to all current configurations, not just to sheets of current.