Question #43440

An electron of mass $m$ (in $\text{kg}$) and charge $-e$ (in $\text{C}$) revolves counterclockwise in the $xy$-plane in a circular orbit of radius $R$ (in $\text{m}$) with a constant angular speed $\omega$ (in $\text{rad s}^{-1}$) around the origin. A closed spherical surface $S$ of radius $r_0$ (in $\text{m}$, where $r_0 \gg R$) is centered at the origin. Let $\Phi_{\text{total}}$ (in $\text{Wb}$) be the net magnetic flux through the entire surface $S$, and $|\Phi_{\text{upper}}|$ (in $\text{Wb}$) be the magnitude of the magnetic flux through the upper hemisphere ($z > 0$) of $S$. Which of the following correctly represents $\Phi_{\text{total}}$ and $|\Phi_{\text{upper}}|$? (Assume vacuum with permeability $\mu_0$ in $\text{T m A}^{-1}$)