Calculating electromagnetic sinusoidal wave

 

Electromagnetic sinusoidal wave propagating in the x direction. Suppose the wave length is 50.0 m and the electric field vibrates in the xy plane with an amplitude of 22.0 V/m.

 

(a) Calculate the frequency of the wave.

(b) the magnetic field B when the electric field has its maximum value in the negative y direction.

(c) Write an expression for B with the correct unit vector, with numerical values for B_max, k, and ω, and with its magnitude in the form like below.

 

풀이)

wavelength λ = 50.0 m

c = 3.00 × 10^8 m / s

 

(a)

Calculate the frequency of the wave

c = f λ

f = c / λ = 3.00 × 10^8 m / s / 50.0 m = 6.00 × 10^6 Hz

 

(b)

The magnetic field B when the electric field has its maximum value in the negative y direction.

max B of -z direction = -E_max / c = -7.33  × 10^-8 T k ( -z direction )

 

(c)

Write an expression for B with the correct unit vector, with numerical values for B_max, k, and ω, and with its magnitude in the form like below.

k = 2π / λ = 2π / 50.0 = 0.126

ω = c × k = 3.77 × 10^7

최종 결과는 아래와 같다.