Electric and magnetic field relationship

[erisedk]

Homework Statement

Why is the following set of electric and magnetic fields invalid?
$E(x, y, z, t)= E_0 \sin{(kz-wt)} \hat{i}$

$B(x, y, z, t) = B_0 \sin{(kz+wt)} \hat{j}$

Homework Equations

The Attempt at a Solution

So, I understand that either both should have (kz-wt) or both should have (kz+wt). Either than the fact that the cross product of electric and magnetic fields is a scalar times a vectors that does not depend on time, whereas here the cross product gives me something like a standing wave in the z direction, I'm not sure why both should have (kz-wt) or both should have (kz+wt). Please help.

 

[TSny]

Have you studied Maxwell's equations?

 

[erisedk]

Yes

 

[TSny]

If you can show that anyone of Maxwell's equations is violated at some point of space at some instant of time, then the fields are invalid.

 

[erisedk]

Thank you! Got it.