Problem 6 (40 points) A parallel plate capacitor with circular plates of radius a, plate spacing d, capacitance C, and i

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Problem 6 40 Points A Parallel Plate Capacitor With Circular Plates Of Radius A Plate Spacing D Capacitance C And I 1 (86.91 KiB) Viewed 56 times

Problem 6 (40 points) A parallel plate capacitor with circular plates of radius a, plate spacing d, capacitance C, and initial charge Qo is discharging through a resistor with resistance R in the circuit shown below. The positive charge is on the upper plate. We know from our study of RC circuits that the charge on the capacitor will be Q(t) = Qoet/RC I(t) Q(t) a P R X-a X C (a) What is the current I(t) flowing through the resistor and what is the power P(t) dissipated in the resistor as a function of time? (b) What is the electric field vector Ē(t) inside the capacitor as a function of time? (c) Is the energy density of the electric field u(t) inside the capacitor increasing or decreasing with time? Briefly justify your answer. (d) Use the Ampere-Maxwell Law to determine the direction and magnitude of the magnetic field vector B(t) at the point P, at position x = -a on the x-axis. Illustrate its direction by a suitable sketch. (e) On the basis of your answer to Part (c), in what direction does the Poynting vector 5 point at the point P ? (f) What is the full expression for the Poynting vector S at the point P ?