1. The wave is propagating in the +x direction. This is evident from the argument of the sine function, (kx + ωt), which indicates a wave moving in the negative x-direction if it were (kx - ωt), but here the positive sign implies propagation in the +x direction when considering the phase velocity. However, standard convention for a wave traveling in the +x direction is (kx - ωt). Given the form (kx + ωt), the wave is actually propagating in the -x direction. The electric field oscillates along the z-axis and the magnetic field along the y-axis, both perpendicular to the direction of propagation (x-axis), making the wave transverse.
2. For the instant shown:
- Electric field magnitude ranking: Point 3 > Point 1 = Point 4 > Point 2
- Point 2 has zero electric field (at node).
- Points 1 and 4 are at the same phase and amplitude.
- Point 3 is at peak amplitude.
- This ranking is consistent with E(x,y,z,t) = E₀ sin(kx + ωt) ẑ, as the field depends only on x and t, not on z. Changing z does not affect the value of E at a fixed x and t.
- Magnetic field magnitude ranking: Point 3 > Point 1 = Point 4 > Point 2
- Point 2 has zero magnetic field (at node).
- Points 1 and 4 are at the same phase and amplitude.
- Point 3 is at peak amplitude.
- This ranking is consistent with B(x,y,z,t) = B₀ sin(kx + ωt) ŷ, as the field depends only on x and t, not on z.
Parent Tip: Review the logic above to help your child master the concept of electromagnetic wave worksheet.
