3. A parallel plate capacitor consists of circular plates of radius r = R. and plate separation D in a vacuum. It is cha

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3 A Parallel Plate Capacitor Consists Of Circular Plates Of Radius R R And Plate Separation D In A Vacuum It Is Cha 1 (76.78 KiB) Viewed 44 times

3. A parallel plate capacitor consists of circular plates of radius r = R. and plate separation D in a vacuum. It is charged with a constant current, I = 10. The charge on the plates is zero at time t = 0. Ignore any fringing fields. (a) Find the charge density on the plates and show that the electric field between the plates as a function of time is given by lot E -2, (1) TR260 where ż points perpendicularly from one plate to the other. (b) Use the Ampere-Maxwell equation to find the magnetic field between the plates. (Hint: This will be a function of the radial distance, r, from the axis.] (C) Write down the standard expression for the total field energy density. Hence find, i. an expression for the field energy density in terms of the quantities given, ii. the total field energy at a time t in a cylindrical 'Gaussian' volume of radius R and length D positioned between the plates, iii. the rate of change of field energy in the Gaussian volume. (d) Write down the standard expression for the Poynting vector and state its meaning. Evaluate the magnitude of the Poynting vector at the curved sur- face of the above Gaussian volume. (e) Find an expression for the total energy flux through the curved surface of the Gaussian volume. (1) Hence show that the power into the capacitor is equivalent to the rate of change of total field energy. State the name of the theorem that this equality supports and provide the equation. In this theorem, which term has been neglected in the problem above?