The electric field of a point dipole antenna. This frame from an animation shows several singular points. Along the axis are -points, where the field lines appear to cross at right angles. In the -plane there are -points close to the antenna propagating inward; farther from the antenna are -points with field lines encircling them propagating away from the antenna.
The electric field of a resonant linear antenna. Along the axis are -points, and in the -plane are -points. All field lines propagate away from the antenna.
Singular points of a resonant antenna. Only a few arbitrary field lines are shown to draw attention to the locations of the singular points. The shaded regions mark zones within which field lines close around the same -point.
Singular points in the equatorial plane. The plots show the radial coordinate of the singular points for antennas with different half-lengths as a function of time. (Both and are dimensionless.) For a resonant antenna, , the plot shows that an -point appears as soon as the current starts to increase at . This -point then propagates away from the antenna. For shorter antennas the plots show that a singular point does not appear immediately. Instead, a singular point develops at a later time at a critical distance from the antenna and immediately splits into an -point and an -point propagating in opposite directions.
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