The electric field vector of an EM wave in free space is given by $$\bar E= \hat y [A\cos{\omega (t- \frac{z}{c}})]$$ where $ \hat y$ is the unit vector along the Y direction.

What will be the magnetic field $\bar H$?

I know the H is oriented in $-x$ direction. Intrinsic impedence, $\eta = \sqrt \frac{\mu_0}{\epsilon_0}$.
The answer is $\bar H = \hat x [-j \frac{1}{\eta } A\sin{\omega (t- \frac{z}{c}})]$. I can't understand why there is $j$

  • $\begingroup$ Using Maxwell's equation in frequency domain you should be able to find H, and see why there's a $j$. Do you know if the the E and H field are in phase or not for a planewave ? $\endgroup$ – EigenDavid Oct 27 '15 at 10:27
  • $\begingroup$ why can't we use this $\bar H = \bar E /\eta =-\hat x [ \frac{1}{\eta } A\cos{\omega (t- \frac{z}{c}})]$ $\endgroup$ – mahes Oct 27 '15 at 13:38
  • $\begingroup$ Where does that come from ? Do you understand what is the physical meaning of the $j$ appearing in your equation ? $\endgroup$ – EigenDavid Oct 27 '15 at 13:51
  • $\begingroup$ its the intrinsic impedence $\eta = E/H$ !!!!! $\endgroup$ – mahes Oct 27 '15 at 14:02