The electromagnetic waves are popularly represented as two sinusoidal waves at right angle to the direction of wave motion. But it is only a representation and not an actual shape right? Let me explain to clarify my question...
Let us say the blue sine wave is showing the strength (lengths of the arrows) and the direction of electric field at the point on the line of propagation. This point is actually on the line labeled Z. Similarly the red sine wave shows the strength (lengths of the arrows) and the direction of magnetic field at the point on the line of propagation. We know that electromagnetic waves can travel in vacuum, which means there is no medium there. Which means there no actual substance sticking out of the line, in the plane of the sine waves shown below.
An alternate representation could instead use intensity of the color at the points on the line itself to represent the strength of the field. May be two colors each could be used to represent positive and negative strength. Thus we may need four colors - 2 for +ve and -ve electric field and 2 for +ve and -ve magnetic file. But in such representation the picture would simply show a line with varying colored point on the line itself. Thus the electromagnetic wave would be a single dimensional line instead of a 3D shape like in the picture.
So my question is in reality what is the actual shape of the electromagnetic wave? Is it just a line with points, where points on it have sinusoidally varying intensity of electric and magnetic field? Or is the wave sinusoidal shapes like the picture shown below.
What happens to the strength of the electric and magnetic field at the points right next to (close to) the line of propagation, which are not on the line itself? What about all the points on a circle at right angles to the line of propagation. What about the points on that circle that are not the same plane as the sine wave?
Also, it is my understanding that the magnetic lines are always loops - no monopoles, then how can a magnetic filed only have one direction at the point. Would such points not be monopoles?
Hope my questions make sense.