Answer to Question #137632 in Electricity and Magnetism for mpho

Question

If the expression for the field quantity E in free space is given by: E= E_0 Sin (ωt-kz)a_x,where E_o,ω&k are constants.Find the remaining three field quantities. (i.e. D, B & H)

Answer 1

$E = E_0 \sin (\omega t-kz)$

In EM wave E and H are connected as

$\sqrt{\epsilon \epsilon_0}\, E = \sqrt{\mu\mu_0}\, H$

So, $H = \sqrt{\frac{\epsilon \epsilon_0}{\mu\mu_0}}\, E = \sqrt{\frac{\epsilon \epsilon_0}{\mu\mu_0}}\, E_0 \sin (\omega t - kz)$

$D = \epsilon \epsilon_0E, \; B = \mu \mu_0 H$, therefore

$D = \epsilon \epsilon_0 E_0 \sin (\omega t-kz)$ and

$B = \sqrt{\epsilon \epsilon_0 \mu \mu_0} \, E_0 \sin (\omega t-kz)$.