Question

Consider a parallel plate capacitor with circular plates of radius a with distance d a between them. The plates are connected to a battery of voltage v . Let r be the resistance in the circuit. Calculate the electric and magnetic elds in the capacitor as a function of r (the radial distance from the axis) and the time t. Calculate the energy density uem and the poynting vector ~s and verify that the continuity equation for energy is satis ed. Determine the total energy in the capacitor as a function of time. Calculate the total power owing into the capacitor by integrating the poynting vector over an appropriate closed surface. Verify that the relation between between the rate of change of the energy and the surface integral of the poynting vector. (you can assume that the rc time constant of the circuit is much larger than a=c, where c is the speed

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