Electromagnetic Fields For Hertzian Dipoles

This Demonstration shows the electromagnetic fields for an electric dipole or a Hertzian dipole, the electric and magnetic fields, the associated energy densities, and the Poynting vector distributions. You can vary the dipole moment, frequency, and time for either a DC or static dipole field.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Snapshot 1: a magnetic field distribution
Snapshot 2: an energy density and Poynting vector distributions
Snapshot 3: a DC electric field
The electromagnetic fields of a Hertzian dipole can be analyzed using the electrical Hertz vector:
where is the dipole moment (a vector in the direction in this analysis), and is the distance to the observation point. The energy density is
The electric and magnetic fields can be calculated as follows:
(in phasor, , ).
In the sinusoidally oscillating dipole of in cylindrical coordinates , the field vectors in the - plane are
, .
The total energy density and Poynting vector are given by
, .
In the graphics, the field strengths are shown by color and the directions are shown by arrows.
The DC fields are obtained from the above equation, with the magnetic field equal to zero.
[1] J. A. Stratton, Electromagnetic Theory, New York: McGraw-Hill, 1941.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+