Oddity in using maxwell's equations in time independent form

[FOIWATER]

I am solving a question that asks me to find an H field in phasor form from the given E field in phasor form

Es = j30(beta)(I)(dl)sin(theta)e^(-j(beta)r) a(theta) V/m

Given that the EM wave propagates in free space.

Why do I get different answers if I :

1) Divide Es by the magnitude of the intrinsic impedance of free space

2) Solve for H field using maxwells equations in phasor form

Should be the same answer right? Since intrinsic impedance is derived using maxwell's equations in my textbook.

any help thanks

 

[FOIWATER]

I am now assuming it is because not only is the wave time varying, it is also propagating.

That leads to the treatment of the field as a wave, and THAT leads to the definition of intrinsic impedance?