Power dissipated in a cylindrical cavity due to a current carrying filament

[nutan123]

Homework Statement

A cylindrical cavity oriented along z axis with length of 2 m has a filament in it upon which a current of 10 A is impressed. Cavity is perfectly conducting whereas it is filled with lossy dielectric. Electric field on the cavity is given as: E=-z(i+j). One has to calculate the power dissipated in the cavity. BTW, the frequency is 5 kHz.

Homework Equations

$$\nabla$$$$\times$$$$\vec{E}$$=-del(B)/del(t)
$$\nabla$$$$\times$$$$\vec{H}$$=del(D)/del(t)+J
S=\vec{E}[/tex]\times[/tex]$$\vec{H}$$

The Attempt at a Solution

It has to do with the Poynting vector. I tried to find the mangetic field from the current but without any value for the permeability and permittivity for the lossy material how can I find the power loss. Is the fact that question provides the electric field is in some way helpful.

 

[gabbagabbahey]

A cylindrical cavity oriented along z axis with length of 2 m has a filament in it upon which a current of 10 A is impressed. Cavity is perfectly conducting whereas it is filled with lossy dielectric.

I assume you mean that the wall of the cavity is perfectly conducting while the cavity itself is filled with a dielectric?

Electric field on the cavity is given as: E=-z(i+j). One has to calculate the power dissipated in the cavity. BTW, the frequency is 5 kHz.

Is $\textbf{E}=-z(\textbf{i}+\textbf{j})$ the field on the cavity's wall, or throughout the cavity's interior?