The electric field of an electromagnetic wave travelling in a medium is given by E = 50 (6 10¹⁴ t - 6 10^6 x) V m ⁻¹ , where x is in metres and t is in seconds. If the relative permittivity of the medium is 4.5 , its relative permeability is (Speed of light in vacuum c = 3 10^8 m s ⁻¹ )

Step-by-step solution

The standard equation for the electric field of an electromagnetic wave is E = E₀ ( t - kx) . Comparing this with the given equation E = 50 (6 10¹⁴ t - 6 10^6 x) , we get: Angular frequency, = 6 10¹⁴ rad s ⁻¹ Wave number, k = 6 10^6 rad m ⁻¹ The speed of the electromagnetic wave in the medium is: v = k = 6 10¹⁴ 6 10^6 = 10^8 m s ⁻¹ The speed of an electromagnetic wave in a medium is related to its relative permeability and permittivity by: v = c _r _r Squaring both sides and solving for relative permeability _r : _