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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)

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The strength of an electric field is a vector, so it has a magnitude and direction, but the magnitude is not spacial. –  fibonatic Jan 25 at 19:26
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3 Answers

The picture below shows 3-D wave with wave fronts.
enter image description here
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.

enter image description here

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. enter image description here

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Here's my visual approach to answering your question: the "spherical electrical waves" that you're referring to are just a way to represent the wave crests of light. When considering the oscillating electric field component of the electromagnetic wave, the individual waves propagate through space symmetrically in all directions when being emitted from a single source, one wave for each direction in 3D space, and when you connect the crests of the propagating waves at a specific instant of time, you obtain the spherical surfaces you're referring to. And when you visualize the crests and troughs of the oscillating magnetic field component of the wave, the same thing will apply, i.e: when you connect the crests of the magnetic waves, you will also obtain spherical surfaces identical to those you obtain when connecting the electric wave crests. So at a certain instant of time, those spherical surfaces rather connect the crests of each individual unidirectional electromagnetic wave emitted from the source, and that over time, span a sphere whose radius increases at a rate equivalent to the speed of light in the respective medium.

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Ok I think I understand your question.

So you're talking about how the electromagnetic waves are always perpendicular to each other, but now, what if we have a spherical electromagnetic wave?

Ok there's a few problem to sort out. First off, electromagnetic waves always travel in a straight line (ignoring effects like general relativity, diffraction (and other scattering processes), etc.). You might already know that, but when bringing up a spherical wave you are probably getting confused. What is this spherical wave and how is it formed? Well, this EM source sounds a lot like the bobbing device in water...at least from what you're describing...causing an outward flux of EM waves in a spherical manner. This actually is just a bunch of EM waves going in a single direction. The photons within the EM waves are traveling in straight lines still. The "spherical" wave is just a bunch of regular EM waves combined together. That explains why the intensity diminishes the farther the radius from your source is.

So instead of picturing waves as 3D, picture them as a bunch of 2D waves strung together. Physics' current understanding is that photons are point particles, so if a point moves in a line (well a curved line I suppose), it is making a 2D shape. The magnetic wave is orthogonal to the electric wave, so the EM wave actually spans 3 dimensions.

So to now answer your question, each part of the EM wave moves in 2 dimensions and you can think of it as a sine wave or a cosine wave plot. Both of them together spans 3 dimensions, but each individual part just spans 2 dimensions.

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"electromagnetic waves always travel in a straight line" - how about diffraction en.wikipedia.org/wiki/Diffraction and other wave optics phenomena? –  Slaviks Jul 29 '13 at 9:07
Ok I know I know lol, you get my point though. They don't run off in random directions by themselves, there's always something acting on them, I'll edit the answer to be more general –  Spaderdabomb Jul 29 '13 at 9:52
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