A homework problem provides that a plane wave is traveling through a medium with a electric permittivity of 2.54 and has an electric field strength $E$ of $5V/m$. I am asked to find the magnetic field strength $H$. I approached this problem with two methods, one using Maxwell's equations and the the other using wave impedance. I got different answers.

Here are my calculations:

Method 1:

$E/B=c\, ,\qquad B=5/c=1.67\times 10^{-8}$

$H=B/\mu=1.57\times 10^{-8}/\mu_0=0.013$

Method 2:

$Z=\sqrt{\epsilon/\mu} = 377\Omega/\sqrt{2.54} = 236.6$

$E = H\times Z, \qquad H = 5/236.6 = .0211$

I do not understand why these answers should be different. I notice that if I use a relative permittivity of 1, I get the same answer with both methods. However, my intuition tells me that the electric permittivity should not affect the magnetic field strength. Where am I wrong here?


Method 1 is incorrect. For a linear dielectric, the ratio of E- to B-field amplitudes is given by the speed of light in the medium.

  • $\begingroup$ That makes sense, thank you! $\endgroup$ Jan 21 '20 at 16:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.