Remember the Poynting vector? The magnitude of this vector gives the amount of energy per second that

Question

flows through a unit area (in the direction it gives) because of the presence of a combination of electric and
magnetic field, like in an electro-magnetic wave. The units for the magnitude of the Poynting vector are W/m2
(or J/s/m2
).
Now, it has been shown that this interpretation for the Poynting vector can also apply to any combination of
electric and magnetic fields, even static fields that do not create any electromagnetic wave! This is a somewhat
surprising result, and this homework is about playing with it for one particular example.
Two circular parallel plates are being charged (starting from their uncharged state) with equal but opposite
charges at a constant rate. The two plates have a radius R, are centered around the z axis, and are parallel
to each other, with a distance d between them. Because they are being charged at a constant rate, the electric
field between the two plates increases linearly from 0 until after a time t0 it reaches a final value E0.
1. Calculate the magnitude and direction of the Poynting vector that is found between the plates, at a
distance r from the center, while the plates are being charged.
2. The Poynting vector gives the energy flow per unit time at one particular position. Integrate this energy
flow to find the total energy per unit time that flows into the volume between the plates.
3. What is the total energy that flows into this volume from time 0 to t0 (when the field changes from 0 to
E0)?
4. What is the energy density found in the volume between the circular plates once the electric field has
reached E0?

Answer 1

Quit cheatin boy