Calculating the Ratio of Electromagnetic Wave Speeds in Vacuum and Materials

[yjk91]

Homework Statement

Electric and magnetic fields in many materials can be analyzed using the same relationships as for fields in vacuum, only substituting relative values of the permittivity and the permeability, ε = κε0 and μ = κmμ0, for their vacuum values, where κ is the dielectric constant and κm the relative permeability of the material. Calculate the ratio of the speed of electromagnetic waves in vacuum to their speed in such a material. (Use the following as necessary: κ, κm, ε0, and μ0.)

The Attempt at a Solution

c= sqrt(epsilon0*mu0)
and by analogy,
v= sqrt(/epsilon/mu)
So,
c/v = 1 / sqrt ( kappa * kappa m)


would the c = 1/ sqrt( epsilon0*mu0)

that would give me 1/(epsilon*mu0)

either of them are wrong..
any hint?

 

[gneill]

c= sqrt(epsilon0*mu0)
and by analogy,
v= sqrt(/epsilon/mu)
So,
c/v = 1 / sqrt ( kappa * kappa m)

Not quite. The relationship between the permeability and permitivity and c is
$$c = \frac{1}{\sqrt{\epsilon_o \; \mu_o}}$$
Make use of the fact that in the material $\epsilon = \kappa \epsilon_o$ and $\mu = \kappa_m \mu_o$

 

[yjk91]

i got it thanks always helping :)