Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 106 rad/s)t]} ˆi.(a) What is the direction of propagation?(b) What is the wavelength λ?(c) What is the frequency ν?(d) What is the amplitude of the magnetic field part of the wave?(e) Write an expression for the magnetic field part of the wave.

(a) The direction of motion is along the negative y-direction, i.e. along -j.

(b) The given equation is compared with the equation,

E = E0 cos (ky + ωt)

⇒ k = 1.8 rad/s

ω = 5.4 x 106 rad/s

λ = 2π/k = (2 x 3.14)/1.8 = 3.492 m

(c) Frequency, ν = ω/2π = 5.4 x 106/(2 x 3.14) = 0.859 x 106 Hz.

(d) Amplitude of the magnetic field, B0 = E0/c

= 3.1/(3 x 108) = 1.03 x 10-8 T= 10.3 x 10-9 T= 10.3 nT.

(e) Bz = B0 cos (ky + ωt)ˆk ={(10.3 nT) cos[(1.8 rad/m)y + (5.4 × 106 rad/s)t]} kˆ