Please confirm the direction of propagation for me.

[yungman]

Please confirm the direction of propagation for me. If the E field is defined as:

$$\vec E \;=\; \frac{\mu_0 k}{2}(ct-|x|)\hat z$$

1) With this equation, the direction of propagation of the E field in both + and – x direction even though the $\vec E = \hat z E_z$?

2) The E field is not propagating along z axis at all even though $\vec E = \hat z E_z$. This only mean the amplitude of the E field is in z direction.
Can someone confirm this for me?

Thanks

Alan

 

[Doc Al]

I'd say you are correct.

 

[torquil]

Yes, the electric field vector points in the z-direction at all spacetime points (EDIT: except where/when it vanishes, of course...)

But how do you define "propagation"?

When plotted against x, the absolute value of the field strength looks like an upside-down V whose tip touches the x-axis at t=0. The pyramid rises linearly in time.

I guess you could use a Maxwell equation to find the B-field, and then form the Poynting vector which then tells you the energy flux.

 

[yungman]

Thanks guys for the quick reply. Yes, it is a inverse pyramid shape but I think the tip touching the z axis at t=0 instead and the base spread out in + and - x direction with time.

 

[PJC01]

Sure, I can confirm the direction of propagation for you based on the given equation. The direction of propagation for an electromagnetic wave is determined by the direction of the electric and magnetic fields, which are perpendicular to each other. In this case, the electric field is defined as \vec E = \hat z E_z, meaning it is pointing in the z direction. Therefore, the direction of propagation for this wave would be in the z direction.

However, it is important to note that the equation provided does not fully describe the propagation of an electromagnetic wave. The equation only represents the electric field component, and the complete description would also include the magnetic field component. So while the electric field is propagating in the z direction, the magnetic field would be propagating in the x or y direction, depending on the specific values of the parameters in the equation.

Furthermore, the equation provided does not specify a specific direction of propagation, as it is dependent on the values of the parameters. The direction of propagation could be in the +x or -x direction, or even in the y direction, depending on the values of the parameters. So to answer your first question, the equation does not specify a specific direction of propagation, as it is dependent on the parameters.

In regards to your second question, the equation does not necessarily mean that the amplitude of the electric field is in the z direction. It simply means that the electric field is pointing in the z direction, and the amplitude would depend on the values of the parameters.

I hope this clarifies the direction of propagation for you. Please let me know if you have any further questions.