Consider current I passing through a resistor of radius r, length L, and resistance R. Determine the strength and direction of the Poynting vector at the surface of the resistor.

Consider current I passing through a resistor of radius r, length L, and resistance R. Show that the flux of the Poynting vector (i.e., the integral of $\overrightarrow{S}\cdot d\overrightarrow{A}$) over the surface of the resistor is I²R. Then give an interpretation of this result.