For a point off the axis, the cross product gives a sine dependence on the angle with the line of motion.
The r vector points toward the point we want to find the contour at. This point is on the contour. The angle the r vector makes with the velocity is theta. Hence, the shape of the contour varies as the sine of the angle for the angle going from zero to pi.
These contours represent a cross section of the fields. There is cylindrical symmetry about the direction of motion of the charge. This symmetry means the colored regions are actually donut-shaped regions about the charge as depicted in the next video clip.
Let me see a closeup of the B field.
Return to Point Charge.