Question
If $$c$$ is the speed of electromagnetic waves in vacuum, its speed in a medium of dielectric constant $$K$$ and relative permeability $${\mu _r}$$ is
A.
$$v = \frac{1}{{\sqrt {{\mu _r}K} }}$$
B.
$$v = c\sqrt {{\mu _r}K} $$
C.
$$v = \frac{c}{{\sqrt {{\mu _r}K} }}$$
D.
$$v = \frac{K}{{\sqrt {{\mu _r}C} }}$$
Answer :
$$v = \frac{c}{{\sqrt {{\mu _r}K} }}$$
Solution :
Speed of light of vacuum $$c = \frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }}$$ and in another medium $$v = \frac{1}{{\sqrt {\mu \varepsilon } }}$$
$$\eqalign{
& \therefore \frac{c}{v} = \sqrt {\frac{{\mu \varepsilon }}{{{\mu _0}{\varepsilon _0}}}} = \sqrt {{\mu _r}K} \cr
& \Rightarrow v = \frac{c}{{\sqrt {{\mu _r}K} }}. \cr} $$