An electromagnetic wave is travelling in a lossless, non-magnetic dielectric medium having a dielectric constant _r = 2.25 . The wavelength of the wave in the medium is 4 m and the peak electric field is 60 V/m. If the wave is propagating along the -y direction and the electric field oscillates along the +z axis, which of the following is the correct vector equation for the magnetic field?

Step-by-step solution

The speed of the electromagnetic wave in the dielectric medium is v = c _r = 3 10^8 2.25 = 3 10^8 1.5 = 2 10^8 m/s. The amplitude of the magnetic field is B₀ = E₀ v = 60 2 10^8 = 3 10⁻⁷ T. The wave vector is k = 2 = 2 4 = 2 rad/m. The angular frequency is = kv = ( 2 ) (2 10^8) = 10^8 rad/s. Since the wave propagates in the -y direction, the phase argument must be of the form (ky + t) . The direction of propagation is given by the direction of E B . Given E = k and v = - j , we have k B = - j . Since k i = j , it fo