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The electric field of a stationary electron is uniform, radially symmetric with straight field lines. However, the electric field of a moving electron still has radial and straight field lines, but they are no longer uniformly distributed, and the effect becomes more pronounced at higher speeds (that is, the field lines become more and more perpendicular to the direction of motion). I found this effect in this applet.

Can someone physically explain to me the cause of this nonuniformity in the field lines? Thanks in advance.

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en.m.wikipedia.org/wiki/Relativistic_electromagnetism it is an effect of relativity, you might want to look at this article a bit –  Dan Jun 12 '13 at 3:20
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Can someone physically explain to me the cause of this nonuniformity in the field lines?

It is due to the Lorentz contraction. The field of a moving point charge is contracted along the line parallel to the motion:

A very important application of the electric field transformation equations is to the field of a single point charge moving with constant velocity. In its rest frame, the electric field of a positive point charge has the same strength in all directions and points directly away from the charge. In some other reference frame the field will appear differently.

In applying the transformation equations to a nonuniform electric field, it is important to record not only the value of the field, but also at what point in space it has this value.

In the rest frame of the particle, the point charge can be imagined to be surrounded by a spherical shell which is also at rest. In our reference frame, however, both the particle and its sphere are moving. Length contraction therefore states that the sphere is deformed into an oblate spheroid, as shown in cross section in Fig 4.

enter image description here

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Where is the quote from? –  Ben Crowell Jun 12 '13 at 4:20
    
@Ben Crowell, the quote is from the link "field of a moving point charge". –  Alfred Centauri Jun 12 '13 at 10:39
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