# Electric and magnetic field relationship

1. Nov 28, 2016

### erisedk

1. The problem statement, all variables and given/known data
Why is the following set of electric and magnetic fields invalid?
$E(x, y, z, t)= E_0 \sin{(kz-wt)} \hat{i}$

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

2. Relevant equations

3. 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.

2. Nov 28, 2016

### TSny

Have you studied Maxwell's equations?

3. Nov 28, 2016

### erisedk

Yes

4. Nov 28, 2016

### TSny

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

5. Nov 29, 2016

### erisedk

Thank you! Got it.

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