A sinusoidal electromagnetic wave is propagating in vacuum. At a given point P and at a particular time, the electric field is in the x direction and the magnetic field is in the -y direction.(a) What is the direction of propagation of the wave?(b) If the intensity of the wave at point P is 7.43kW/cm2, what is the electric and magnetic field amplitude at that point? (c = 3.00 ×108 m/s, μ0 = 4π× 10-7 T · m/A,ε0 = 8.85 × 10-12 C2/N · m2)

According to right hand rule, your finger (direction of electric field) would be pointing in the positive x-axis i.e towards your right let your palms be face toward the direction of the magnetic field i.e negative y-axis (toward the ground ) Then anywhere your thumb stretched out is facing is the direction of propagation of the wave here in this case is the negative z -axis

The Intensity of the wave is mathematically represented as

[tex]I = \frac{1}{2} c \epsilon _O E_{rms}^2[/tex]

Given that [tex]I = 7.43 \frac{kW}{cm^2} = 7.43 \frac{*10^3}{*10^-{4} }= 7.43*10^7 \frac{W}{m^2}[/tex]

Making [tex]E_{rms}[/tex] the subject we have

[tex]E_{rms} = \sqrt{\frac{I}{0.5*c*\epsilon_o} }[/tex]

Substituting values as given on the question

[tex]E_{rms} = \sqrt{\frac{7.43 *10^7[\frac{W}{m^2} ]}{0.5 * 3.08*10^8 *8.85*10^{-12}} }[/tex]

[tex]= 2.37*10^5 \ V/m[/tex]

The amplitude of the electric field is mathematically represented as

[tex]A_E = \sqrt{2} * E_{rms}[/tex]

[tex]= \sqrt{2} * 2.37*10^5[/tex]

[tex]A_E= 3.35*10^5 V/m[/tex]

The amplitude of the magnetic field is mathematically represented as

[tex]A_M = \frac{A_E}{c}[/tex]

Substituting value

[tex]A_M = \frac{3.35 *10^5}{3.0*10^8}[/tex]

[tex]A_M= 1.12 *10^{-3} T[/tex]