Electromagnetic Waves

Olympiad (NSEP) level, one or more correct, hard

3 of 165

Question 3 of 165

A plane electromagnetic wave in free space has electric field E⃗=E0j^cos⁡(kx−ωt)\vec{E} = E_0 \hat{j} \cos(kx - \omega t). Which of the following statements are TRUE?

Show answer and solution

Answer: (A) Electric and magnetic energy densities are equal at all points, (B) The magnetic field is B⃗=E0ck^cos⁡(kx−ωt)\vec{B} = \frac{E_0}{c} \hat{k} \cos(kx - \omega t), (C) The wave propagates along the +x+x-direction, (D) The time-averaged Poynting vector is ⟨S⃗⟩=E022μ0ci^\langle \vec{S} \rangle = \frac{E_0^2}{2 \mu_0 c} \hat{i}

Direction of propagation is E^×B^=j^×k^=i^\hat{E} \times \hat{B} = \hat{j} \times \hat{k} = \hat{i} (+x+x-axis). Average intensity is E022μ0c\frac{E_0^2}{2\mu_0 c}.
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