Chapter 16, Problem 106CP

A parallel-plate capacitor with plate separation d is connected to a source of emf that places a time-dependent voltage V(t) across its circular plates of radius r₀and area

(a) Write an expression for the time rate of change of energy inside the capacitor in terms of V(t) and dV(t)/ dt.

(b) Assuming that V(t) is increasing with time, identify the directions of the elecuic field lines inside the capacitor and of the magnetic field lines at the edge of the region between the plates, and then the direction of the Poynting vector

   $\stackrel{\to }{S}$ at this location.

(c) Obtain expressions for the time dependence of E(t), for

B(t) from the displacement current, and for the magnitude of the Poynting vector at the edge of the region between the plates.

(d) From $\stackrel{\to }{S}$ , obtain an expression In terms of ‘(t) and dV(t)/dt for the rate at which electromagnetic field energy the region between the plates.

(e) Compare the results of pails (a) and (d) and explain the relationship between them.