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 r0 and area A = πr0 2 (see below). (a) Write an expression for the time rate of change ofenergy inside the capacitor in terms of V(t) and dV(t)/dt.(b) Assuming that V(t) is increasing with time, identify thedirections of the electric field lines inside the capacitor andof the magnetic field lines at the edge of the region betweenthe plates, and then the direction of the Poynting vectorS →at this location.(c) Obtain expressions for the time dependence of E(t), forB(t) from the displacement current, and for the magnitudeof the Poynting vector at the edge of the region between theplates.(d) From S → , obtain an expression in terms of V(t) anddV(t)/dt for the rate at which electromagnetic field energyenters the region between the plates.(e) Compare the results of parts (a) and (d) and explain therelationship between them.
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 r0 and area A = πr0 2 (see below).
(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 electric 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
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 S → , obtain an expression in terms of V(t) and
dV(t)/dt for the rate at which
enters the region between the plates.
(e) Compare the results of parts (a) and (d) and explain the
relationship between them.
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