Consider how the radiated fields are produced. From Maxwell's equations we know that the changing electric and magnetic fields are inextricably linked.
The radiated part of the electric field depends on the rate of change of the magnetic field. To find where the electric field is strong, we must find where the change in the magnetic field is the greatest. Recall that along the line of motion of the particle the magnetic field is zero and is strongest perpendicular to that line.
As the velocity of the particle increases, the magnetic field will get stronger and form a swirling field around the axis of motion.
For this simple example, the region where B is getting stronger is where most of the E is radiated. Because of this linkage, the magnitude of E and B will be virtually identical in appearance, even though the directions are different. The direction of E opposes the acceleration, but the direction of B circulates around E.
Go to Exercise 1.