A circular parallel-plate capacitor of radius a and plate separation d is connected in series with a resistor R and a switch, initially open, to a constant voltage source V0. The switch is closed at time t = 0. Assuming that the charging time of the capacitor, τ = CR, is very long compared with a/c and that d << a (C is the capacitance and c is the velocity of light), find an expression for the displacement current density as a function of time. Obtain an expression for the magnetic flux density B as a function of time and of position between the capacitor plates.