1. Hertzian Dipole Current Density Vector Magnetic Potential
Antennas
Hertzian Dipole
Current Density
Vector Magnetic Potential
Electric and Magnetic Fields
Antenna Characteristics

2. Hertzian Dipole Step 1: Current Density
Let us consider a short line of current placed along the z-axis.
Where the phasor
The stored charge at the ends resembles an electric dipole, and the short line of oscillating current is then referred to as a Hertzian Dipole.
The current density at the origin seen by the observation point is
A differential volume of this current element is

3. Hertzian Dipole Step 2: Vector Magnetic Potential
The vector magnetic potential equation is
A key assumption for the Hertzian dipole is that it is very short so
The unit vector az can be converted to its equivalent direction in spherical coordinates using the transformation equations in Appendix B.
This is the retarded vector magnetic potential at the observation point resulting from the Hertzian dipole element oriented in the +az direction at the origin.

4. Hertzian Dipole Step 3: Electric and Magnetic Fields
The magnetic field is given by
It is useful to group  and r together
The electric field is given by
In the far-field, we can neglect the second term.
Far-field condition:

5. Hertzian Dipole Step 4: Antenna Parameters Power Density:
Maximum Power Density:
Antenna Pattern Solid Angle:
Directivity:

6. The power radiated by the antenna is
Hertzian Dipole
Step 4: Antenna Parameters
Total Radiated Power and Radiation Resistance :
The total power radiated by a Hertzian dipole can be calculated by
The power radiated by the antenna is
Circuit Analysis
Field Analysis

7. Hertzian Dipole - Example
Electric Field:
Power density:
Maximum Power density:
Normalized Power density

8. Example
Antenna Pattern Solid Angle:
Radiated Power:
Radiated Resistance: