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# Spherical wave animation (dipole e/m radiation)

Posted by Happy Hippo
on
4/01/2013 02:38:00 am

I recently was shown an equation for a spherical wave, given as an E-field vector field:

It looked interesting, so I decided to try to visualize it to understand better how would such a vector field, directed along phi unit vector, generate a spherical wave? For this I used MATLAB MuPad application to convert the equation to Cartesian form and then generated some plots.

Slice plots of E-field magnitude:

Iso- surfaces of magnitude of E-field:

High intensity isosurfaces

Medium intensity isosurfaces

Low intensity isosurface (becomes more spherical) , as seen with circles here: http://www.1stardrive.com/solar/mechs8.gif

These "doughnut" shape features shrink in size because the intensity decreases with distance (as 1/r^2), however, if we normalize the intensity by r^2, we will now see where each individual point of E-field propagates with time, and the "doughnuts" will just expand, as shown on the right.

Some more:

B-field and Poynting vector intensities are coming soon !

It looked interesting, so I decided to try to visualize it to understand better how would such a vector field, directed along phi unit vector, generate a spherical wave? For this I used MATLAB MuPad application to convert the equation to Cartesian form and then generated some plots.

Slice plots of E-field magnitude:

Iso- surfaces of magnitude of E-field:

High intensity isosurfaces

Medium intensity isosurfaces

Low intensity isosurface (becomes more spherical) , as seen with circles here: http://www.1stardrive.com/solar/mechs8.gif

These "doughnut" shape features shrink in size because the intensity decreases with distance (as 1/r^2), however, if we normalize the intensity by r^2, we will now see where each individual point of E-field propagates with time, and the "doughnuts" will just expand, as shown on the right.

Some more:

B-field and Poynting vector intensities are coming soon !