Question

A uniform electric field is directed axially in a cylindrical region that includes a rectangular loop of wire with total resistance R$R$. This loop has radially oriented width a$a$ and axially oriented length b$b$, and sits tight against the cylinder axis, as shown in (Figure 1). The electric field is zero at time t$t$ = 0 and then increases in time according to E⃗ =ηt2k^$\overrightarrow{E}=\eta t^2\hat{k}$, where η$\eta$ is a constant with units of V/(m⋅s2)$\mathrm{V}/(\mathrm{m}\cdot {\mathrm{s}}^2)$.