As shown in the Fig 7.2, the current element is located at the origin and oriented in the z-direction. We consider the time harmonic case where the current varies sinusoidally with time and I represents the current phasor. For a z-directed current density located in free space, from equation (7.7) we can write

................................(7.10)

In the source free region the wave equation reduces to

............................(7.11)

Since the current element is infinitesimally small, it can be regarded as a point source so that away from the source will be a function of r only. Therefore equation(7.11) can be written as:

Fundamentals of Antennas and Radiating systems