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Electric field of a point charge in uniform motion

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In Griffiths Chapter 12, pg 527:

Suppose a point charge is moving along x, we obtain the following E-fields:

Questions

1. Is the vector R solely in the x-y plane?

2. What happened to the coordinate 'z' ?

3. Why are they only doing things in the 2-D plane? Can we use rotational symmetry somewhere?


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