# At what point in space do we measure the electric field of an electromagnetic wave?

In an electromagnetic wave, the electric field varies in magnitude and direction. This electric field is at some point in space, point in the direction perpendicular to its velocity. See the image attached below.

When we say that the electric field has a value $$\mathbf{E}$$, do we mean at point $$P$$?

What are the values of electric field at points $$Q$$ and $$R$$?

• You can measure it at any point you like. – The Photon Nov 17 at 23:19
• The drawing suggests that you might be thinking of the electric field vector as a displacement in space. It isn't. At every point in space, the electric field vector has a direction and a magnitude, but it doesn't represent any kind of spatial displacement. It's not like a wave on the surface of water. – Chiral Anomaly Nov 17 at 23:53
• $\boldsymbol{E}=\boldsymbol{E(r,t)}$.So you can measure it any point(P,Q or R) but it is varying with time. – baponkar Nov 19 at 12:47

2.: Not enough information. It depends on the transverse amplitude distribution. If it's a plane wave, the amplitude is the same as at P. Otherwise we don't know. We'd need to know what type of beam it is (Gaussian, Bessel, etc), the characteristics of the beam (transverse size, etc), and what part of the beam the vector $$\vec{v}$$ goes through.
In a plane wave (the most common type of wave you'll see in a physics classroom), the field will be the same, in both magnitude and direction, throughout the whole plane perpendicular to its direction of motion. So in your picture, it will be the same at $$P$$, $$Q$$ and $$R$$. But a real light beam will have a finite extent; the amplitude will drop to zero eventually. Also, the waves in $$P$$, $$Q$$ and $$R$$ might not be related to each other at all. The more related they are, the more spatial coherence the whole wave has.