A uniform electric field is directed axially in a cylindrical region that includes a rectangular loop of wire with total resistance R. This loop has radially oriented width a and axially oriented length b, and sits tight against the cylinder axis, as shown in (Figure 1). The electric field is zero at time t = 0 and then increases in time according to E⃗ =(ηt^2)k, where η is a constant with units of V/(m⋅s2) and k is the unit vector.
A What is the magnitude of the displacement current through a circular loop centered on the cylinder axis with radius r≤a , at time t ?
B Use Ampere's law to determine the magnitude of the magnetic field a distance r≤a from the cylinder axis at time t .
C What is the magnetic flux at time t through the rectangular wire loop?
D What magnitude of current flows in the wire?
E Does the current flow clockwise or counterclockwise from the perspective shown in the figure?