$11\mathrm{.}8.$ Application: Displacement Current. An AC generator operating at a frequency of $1$ GHz is connected with a wire to a small conducting sphere of radius $a=10mm$ at some distance away $($see Figure $11\mathrm{.}6).$ If the sphere is in free space, calculate the current in the wire. Neglect any effect the ground may have. The generator generates a sinusoidal voltage of amplitude $100$ V $.$

Figure $11\mathrm{.}6$