2. Fields around time-varying currents (a) An infinitely long cylindrical shell of radius R carries a spatially uniform but time- dependent solenoid-like surface current density K(t) = Ko(t/T)6, where K, and T are constants. Find the electric and magnetic fields everywhere in space. Hint: begin with a simple guess for the magnetic field outside the solenoid. (b) An infinitely long cylindrical shell of radius R carries a spatially uniform but time- dependent wire-like surface current density K(t) = Ko(t/T)z, where K, and T are constants. Find the electric and magnetic fields everywhere in space. Hint: You may assume the electric field inside the cylinder in zero