Electromanetic waves travel in a medium with a speed of `2 xx 10^(8) ms^(-1)`. The relative magnetic permeability of the medium is 1. Find the relative electrical permittivity.

Explanation

Given `v = 2 xx 10^(8) ms^(-1)` and `mu_(r) = 1`
The speed of electromagnetic waves in a medium is given by
`v = (1)/(sqrt(muepsi))…….(i)`
where, `mu` and `epsi` are absolute permeability and absole permittivity of the medium respectively.
Now, `mu = mu_(0)mu_(r)` and `epsi = epsiepsi_(0)`
`:.` Eq. (i) becomes, `v = (1)/(sqrt(mu_(0)mu_(r)epsi_(0)epsi_(r))) = (1)/(sqrt(mu_(0)epsi_(0))) xx (1)/(sqrt(mu_(r)epsi_(r)))`
`rArr v = (c)/(sqrt(mu_(r)epsi_(r)))` , `[ :' c = (1)/(sqrt(mu_(0)epsi_(0)))]`
On squaring both sides, we get `epsi_(r) = (c^(2))/(v^(2)mu_(r)) = ((3 xx 10^(8))^(2))/((2 xx 10^(8))^(2)xx1) = 2.25`