Find B-Field from E-Field: Correct Answer Revealed

[radiator]

Homework Statement

E = 20 cos($$\omega$$t-50x) $$\widehat{y}$$ find H in free space?

Homework Equations

I used ($$\nabla$$ X E ) = -dB/dt , and then integrated that expression with respect to t , for some reason I am getting an incorrect answer ?!

The Attempt at a Solution

the correct answer is H = 0.4 w*(eps) *cos($$\omega$$t-50x) $$\widehat{z}$$

 

[Pythagorean]

I used ($$\nabla$$ X E ) = -dB/dt , and then integrated that expression with respect to t , for some reason I am getting an incorrect answer ?!

The Attempt at a Solution

the correct answer is H = 0.4 w*(eps) *cos($$\omega$$t-50x) $$\widehat{z}$$

remember that H and B are not the same.

D = eps*E
and
H = B/mu

also:

( $$\nabla$$ X H ) = -dD/dt

or for linear media:( $$\nabla$$ X B ) = mu*eps*dE/dt
also remember that the curl pertains to spatial, not temporal derivatives.