Question #42715

A straight conducting wire is uniformly accelerated along its length (the $+x$ direction) with a constant acceleration $a_0$. A uniform constant electric field of magnitude $E$ is applied along the $+x$ direction within the wire. The conduction electrons have mass $m$, charge $-e$, and an average relaxation time $\tau$ between successive collisions with the lattice. Assume the standard Drude model where electrons lose their entire drift momentum relative to the lattice upon each collision, and the steady-state drift velocity is given by $\vec{v}_d = \vec{F}_{\text{net}}\tau/m$. In the non-inertial frame of the accelerating wire, let $P_{\text{heat}}$ be the average rate of heat dissipation per electron, and $P_E$ be the average rate at which the electric field does work on a single electron. Which of the following expressions correctly represents the difference $(P_{\text{heat}} - P_E)$? (All given quantities are in standard SI units)