You might know already that it is possible to think of theenergy stored in a charged capacitor as being stored in theelectric field between the plates. we will explore this idea byconsidering the flow of energy into the space between the platesduring the charging process. the capacitor is charged by a constantcurrent i, which flows for a time t. at the beginning of this charging process (t =0), there is no charge on the plates.

the poynting vector s_vec gives the flow of electromagnetic energy per unit areaper unit time and is defined in terms of the electric field vectore_vec and the magnetic field vector b_vec by the relation

\vec{s} = \frac{1}{\mu_0} \vec{e}\times\vec{b}.

find an expression for the magnitude of the poynting vector|s(t)| on the surface that connects the edges of the twocircular plates.

express the magnitude of the poyntingvector in terms of t, i,r, pi, epsilon_0, and other variables and parameters of the problem. ignore all fringing effects.
|s(t)| =\frac{i^{2}}{\left(2{\pi}^{2}\righ t)\left(r^{3}\right){\epsilon}_{0}} t
correct
my answersreview part

part b
calculate the the total amount of energyuthat flows into the space between the capacitor plates fromt=0 to t=t, by first integrating the poynting vector over thesurface that connects the edges of the two circular plates, andthen integrating over time.
express the total amount of energy interms of t, i,r, pi, epsilon_0, and other variables and parameters of the problem. ignore all fringing effects.
u =