How to visualize electromagnetic waves? Can someone please explain to me how to visualize an electromagnetic wave in 3D space? I have struggled for a long time now trying to understand how a WiFi signal could reach a device if it looks like a "crosshair" shape and travels in one direction. I do however understand the concept of it being omnidirectional (like waves on a pond).
Let me put it this way, say there is a room, and in the center, a single antenna (such as a WiFi signal) that emits an omnidirectional wave. Does the wave amplitude represent how high the wave goes (to the ceiling)? And howcome it looks like a sphere? Why is it shaped like that, does the electric field vector play a role in this shape?
 A: 
Can someone please explain to me how to visualize an electromagnetic wave in 3D space?

The wikipedia article on electromagnetic radiation is clear enough.


The electromagnetic waves that compose electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized EMR wave propagating from left to right (X axis). The electric field is in a vertical plane (Z axis) and the magnetic field in a horizontal plane (Y axis). The electric and magnetic fields in EMR waves are always in phase and at 90 degrees to each other.

This is one optical ray from the source,and the colored part is how the functions describing the strength of the electric and magnetic field change in space with a wave pattern.
You ask:

Does the wave amplitude represent how high the wave goes (to the ceiling)? 

No, what are waving are the strengths of the E and B fields.

And howcome it looks like a sphere? Why is it shaped like that,

A source of electromagnetic waves, like an antenna impose a pattern that releases in spherical optical rays the wave depicted above , because of the geometry and the nature of wave solutions to the elecromagnetic equations. As the other answer says, it is a three dimensional radiation and will be distributed radially , similar to a two dimensional source of a disturbance of the surface of a lake  which is distributed circularly. 

does the electric field vector play a role in this shape? 

Yes, it is the electric and magnetic fields that vary in space as the wave propagates. 


This 3D animation shows a plane linearly polarized wave propagating from left to right. Note that the electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together

A: A pond is 2D, so you have 2D circles. EM waves travel in 3D, so there are spherical (if the emitter is isotropic). Here the antenna impose an orientation. But it simply means that the intensity in an non-horizontal direction is modulated by the appearant cross section of the antenna you see from that angle, i.e., the amplitude is modulated by the cosine of the elevation angle.
