Electric field of a point charge in uniform motion

[unscientific]

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?

 

[unscientific]

When instead, I assume the particle to be moving along z-axis it fixes everything!

and i use x=Rsinθcosø, y = Rsinθsinø, z = R cos ø

The end result turns out beautifully to be the one as described, in 3 dimensions:

I suspect that since Polar coordinates is usually defined with θ as angle between R and z-axis and ø as angle in x-y plane, everything matches.

 

[unscientific]

bumpp