(a) Given: E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 10⁶ rad/s)t]}

_{As it is clear from the above electric field vector, that electric field is in the negative x direction. Therefore, the direction of propagation of the vector will be in negative y-direction i.e. –j.}

(b) As we know that the general equation for electric field vector in the positive x-direction is:

..........(i)

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_{..............(ii)}

Comparing equation (i) and (ii), we get

E₀ = 3.1 N

(c) Angular frequency ω = 5.4 × 10⁶ rad/s

Wave number i.e. k = 1.8 rad/m

Wavelength of the wave can be calculated as follows:

λ = 2π/k

(d) Angular frequency of the wave can be expressed as follows:

ω = 2π v

⇒ 5.4 × 10⁶ = 2 × 3.14 × v

⇒

⇒

⇒ V = 0.86 × 10⁶ Hz

(e) Magnetic field strength can be calculated as follows:

B₀ = E₀/c

⇒

⇒ B₀ = 1.03 × 10^-7 T

(f) Since magnetic field vector is in the negative z-direction, the general equation for magnetic field vector can be written as follows:

The expression for the magnetic field part of the wave can be written as follows:

B = B₀ cos (ky + wt) k

B = {1.03 × 10^-7 cos [(1.8 rad/m)y + (5.4 × 10⁶ rad/s)t]}k