The magnetic field of a plane electromagnetic wave is
B = B₀ sin[2πνt-(2πx / λ)] ĵ.
The wave propagates in the +x direction through a medium in which the wave speed is νλ. Which expression gives the associated electric field?

Question

The magnetic field of a plane electromagnetic wave is

B = B₀ sin[2πνt-(2πx / λ)] ĵ.

The wave propagates in the +x direction through a medium in which the wave speed is νλ. Which expression gives the associated electric field?

G1 Physics · Accepted Answer

For an electromagnetic wave, E, B and the direction of propagation are mutually perpendicular, with E×B pointing in the direction of propagation. The wave propagates along +x and B is along +y. Therefore E must point along -z because (-k̂)×ĵ = î. Also, the field magnitudes satisfy E₀ ÷ B₀ = wave speed. The wave speed is v(wave) = νλ. Hence, E₀ = νλB₀. Therefore, E = -νλB₀ sin[2πνt-(2πx ÷ λ)] k̂. Correct option: A.