A long cylindrical conductor of radius 'R' and electrical conductivity σ is immersed in a uniform electric field 'E' directed along its axis, imposed by a distant battery. By evaluating an appropiate term in the integral form of the poynting theorm, show that the power dissipated to heat (the joule heating) in length 'l' of the conductor is:
P = IV
The Attempt at a Solution
I think the integral term which is asking to evaluate is:
∫jf . E dV where jf is the conduction current density and dv is the whole volume of the cylinder.