Question #43402

A rigid circular wire loop of radius $R$ and cross-sectional area $A$ lies in the $x-y$ plane, centered at the origin. The wire contains a free electron density $n$, and the electrons have a relaxation time $\tau$ and mass $m_e$. A uniform azimuthal electric field $E_0$ is established in the wire, driving a steady base conventional current $I_0$ in the counter-clockwise direction ($+\hat{\theta}$). The entire loop is placed inside a rocket that is accelerating with a constant acceleration $\vec{a} = a_0 \hat{i}$ relative to an inertial frame. Assuming steady state is reached in the rocket's frame, find the net magnetic field $\vec{B}$ at a point $(0, 0, z)$ on the axis of the loop. (Given: $e$ is the magnitude of the elementary charge, $\mu_0$ is the vacuum permeability. Ignore the self-magnetic field's effect on the drift velocity).