Question

A point charge q moves uniformly and rectilinearly with a relativistic velocity equal to a β fraction of the velocity of light (β = v/c). Find the electric field strength E produced by the charge at the point whose radius vector relative to the charge is equal to r and forms an angle θ with its velocity vector.

Answer 1

Suppose the charge qr moves in the positive direction of the x-axis of the frame K. Let us go over to the moving frame K', at whose origin the charge is at rest. We take the x and x' axes of the two frames to be coincident, and the y & y' axes, to be parallel.

and this has the following components,

Now let us go back to the frame K. At the moment, when the origins of the two frames coincide, we take t = 0. Then,