Effect of a linear medium on a plane wave's electric and magnetic fields using wave impedance

Question

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?

Answer 1

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.