A long and thick, cylindrical conducting rod with radius R is centered on the z axis of a cylindrical coordinate system as shown in the figure. A narrow saw cut is made in the rod at z = zg. A conduction current i(f), increasing with time and given by i(f) = kf (i.e., a ramp), flows toward the right in the rod; k is a (positive) proportionality constant with units C/s%. At time = 0 s there is no charge on the cut faces near z = z,. Neglect fringing effects (i.e., assume the gap to be an ideal parallel-plate capacitor). Find: 1) The magnitude of the charge on the left face, as a function of time, and the electric field E in the gap as a function of time. [15 points] 2) The direction and magnitude of the magnetic field induced within the gap, B , for r