Plane Wave propogation dependent on space and timez

[fred3142]

Hi,

I've been looking at some animations of plane waves, and I really cannot see why a plane wave's electric field is dependent on both t and z. Isn't z a function of t? I would've thought that z could be written in terms of t. Can it? Is there no link between z and t?

$$
\mathbf{E}(x,y,z;t) = \mathbf{E}_o e^{\jmath(\omega t - kz)}
$$

 

[Nugatory]

Hi,

I've been looking at some animations of plane waves, and I really cannot see why a plane wave's electric field is dependent on both t and z. Isn't z a function of t? I would've thought that z could be written in terms of t. Can it? Is there no link between z and t?

$$
\mathbf{E}(x,y,z;t) = \mathbf{E}_o e^{\jmath(\omega t - kz)}
$$

Pick a particular value of t and plug it in, and you'll have an equation in which z is the only variable; that is, you can use it to find out what the value of E will be at any point in space at that particular time.

Conversely, pick a value of z and and plug it in, and you'll have an equation in which t is the only variable; that is, you can use it to find out what the value of E will be at that point in space at any time.

Leave both z and t as independent variables and you have an equation which tells you what the value of E is at any time (pick your t value) and any place (pick your z value).

 

[frogguy]

Hi,
In a plane wave, E is not plane, but the surface where all the points of the field are in phase is a plane. In the equation, if you pick a value of t, the phase is the same for a given value of z whatever x and y are : a plane.