Consider current I passing through a resistor of radius r, length L, and resistance R.
a. Determine the electric and magnetic fields at the surface of the resistor. Assume that the electric field is uniform throughout, including at the surface.
b. Determine the strength and direction of the Poynting vector at the surface of the resistor.
c. Show that the flux of the Poynting vector (i.e., the integral of S · dA) over the surface of the resistor is I²R. Then give an interpretation of this result.