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

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?