# Cylindrical Light Waves and how the wave equation changes

My homework asks "Suppose the source was a long thin ﬁlament so that cylindrical waves were generated. Describe how your equations would change for this situation."

The equations we have that they refer to are those of earlier questions $$(\mathbf{E}=E_0 cos(kx-wt) \mathbf{\hat{j}}$$ and $$\mathbf{E}=\frac{E_0}{c} cos(kx-wt)\mathbf{\hat{k}})$$.

I'm confused because we haven't learned what cylindrical waves are? My guess is they mean a circular wave (that makes a cylindrical shape as it propagates). In this case the equations would change as there would need to be a phase difference between the electric and magnetic fields to achieve this polarization.

Do you think I am right in assuming they mean circular waves?

• I'm guessing they mean either cylindrical or elliptical. In either case you'd have a combination of cose and sine i suspect to account for this. Apr 10, 2019 at 9:19

## 1 Answer

From the way I understand the question, what they mean by cylindrical waves is waves that have cylindrical wavefronts. Just search on Google cylindrical wavefronts for images.

In this question, they are trying to get you to think of wavefronts that are concentric cylindrical surfaces whose axes are the thin filament. With this in mind, try using cylindrical polar coordinates and think about how the equations for electric fields will change.