The electric field of an EM wave is given by Ez= Em sin(k y-ωt+π/ 6), Ex=0, and Ez=0 . (a) In wh

step 1 We have EZ equals em sign KY minus omega t plus pi over six. And from here we can see that it tr

The electric field of an EM wave is given by Ez= Em sin(k...

The electric field of an EM wave is given by $E_{z}=$ $E_{\mathrm{m}} \sin (k y-\omega t+\pi / 6), E_{x}=0,$ and $E_{z}=0 .$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the magnetic field of this wave.

Key Concepts

Wave Propagation Direction

This concept deals with determining the direction in which an electromagnetic wave travels by analyzing the phase factor of its wave equation. The phase term, commonly written in the form k·r - ?t + ?, indicates that the wave advances in the direction of the wave vector k, as each surface of constant phase (wavefront) moves outward along k.

Phase Factor in Wave Equations

The sinusoidal phase factor in a wave equation encapsulates the spatial and temporal oscillations of the wave. Understanding how the arguments of sine or cosine functions, such as k·r - ?t + ?, influence the behavior of the wave is essential for determining properties like propagation direction and oscillation characteristics.

Orthogonality of Fields

A key property of electromagnetic waves is that the electric field, the magnetic field, and the direction of propagation are all mutually perpendicular. This orthogonality, mandated by Maxwell's equations, is foundational in describing the transverse nature of electromagnetic radiation.

Relationship Between Electric and Magnetic Field Magnitudes

The amplitudes of the electric and magnetic fields in an electromagnetic wave are interconnected by the speed of light. In free space, the magnitude of the magnetic field is given by the electric field magnitude divided by the speed of light (B = E/c), reflecting the intrinsic link between these fields as predicted by Maxwell's equations.

Please give Ace some feedback