Question #42610

A closed circuit loop of area $A$ and total resistance $R$ contains a parallel-plate capacitor of capacitance $C$. The loop lies in the $xy$-plane and is subjected to a uniform external magnetic field $\vec{B}_{\text{ext}}(t) = B_0 \cos(\omega t) \hat{k}$. The time-varying magnetic flux induces a conduction current in the loop, which in turn creates a displacement current $I_d(t)$ between the capacitor plates. If $I_d(t)$ is expressed as $I_{\text{max}} \cos(\omega t + \phi)$ with $I_{\text{max}} > 0$, and its positive direction is defined by the right-hand rule relative to $\hat{k}$, what is the phase constant $\phi$?