The Traveling Electromagnetic Wave, Qualitatively — Question 3

Question 3

The sign inside the phase identifies the direction of motion

Two scalar profiles are $E_A=E_0\cos(kx-\omega t)$ and $E_B=E_0\cos(kx+\omega t)$, with positive k and omega and omega/k=c. Both electric fields point along y.

1. Follow a constant phase to find each propagation velocity.

2. Find the corresponding signed magnetic fields and explain why using the same Bz sign for both profiles fails.

Question 3 - Solution

The sign inside the phase identifies the direction of motion

(a) Method and calculation

$$kx-\omega t=\phi\Rightarrow\boxed{dx/dt=+\omega/k=+c}.$$$$kx+\omega t=\phi\Rightarrow\boxed{dx/dt=-\omega/k=-c}.$$

(b) Interpretation and further calculation

$$\boxed{B_{Az}=E_A/c,\qquad B_{Bz}=-E_B/c}.$$$$\hat y\times\hat z=\hat x,\quad\hat y\times(-\hat z)=-\hat x.$$

Physical check

The sign relation between B and E changes when the propagation direction changes, even if their electric polarization is identical.