An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is __________× 10⁷ m/s.

Concept: 

Since speed of light in a medium is given by:

 \(v = \frac{1}{\sqrt{μ ϵ }} = \frac{1}{\sqrt{μ _{r}μ _{0}ϵ _{r}ϵ _{0}}} \)

 \(v = \frac{c}{\sqrt{ϵ _{r}μ _{r}}}\)    ----(1)

where,

 \(c = \frac{1}{\sqrt{ϵ _{0}μ _{0}}}\) = speed of light = 3 × 10⁸ m/s

Calculation:

Given: 

Frequency of electromagnetic wave = 5 GHz = 5 × 109 Hz

Relative electric permeability \(ϵ _{r} = \) 2 

Relative magnetic permeability \(μ _{r}=\) 2

The velocity of medium =? 

The velocity of medium is:

 \(v = \frac{c}{\sqrt{ϵ _{r}μ _{r}}}\)

Here ϵ_r = 2, μ_r = 2  

So that, \(\Rightarrow v= \frac{c}{\sqrt{2× 2}} = c/2 \)

v = 1.5 × 108 m/s = 15 × 10⁷ m/s = velocity of medium.

Hence, answer is = 15