I am having a hard time picturing waves, the image that comes to mind is a bobbing device submerged in still water which generates pulses in all directions (similarly in air). Then how can a wave be two dimensional? The classic image of an electromagnetic wave is a 3D wave function, x-y represent the electrical component, z-x represents the magnetic component. But this is a wave function, so its just a plot, and that is not how I should picture it (or is it?). So in real life, if I have a source of EMR in space, I can imagine concentric spheres of Electrical fields, but what about the magnetic fields? How will they be perpendicular to a sphere of electric fields? Can someone help me picture EMR? Thanks! (apologies in advance for the noobish language, I am an absolute beginner to physics)
Answer
The picture below shows 3-D wave with wave fronts.
Imagine holding the wave fronts and turning into half a circle. When you look into the same 3-D wave from the upside now, you will just see half circle. This is your 2-D wave. The same you see in books with half circles (wave fronts) emanating from a point.
In the following picture, take off the components of the electric and magnetic field below the line of propagation from your mind. See the upper half, if you increase the length of wave front you will get the first picture. Similarly it applies to the other component. I hope it helped. 
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