An electromagnetic wave in a vacuum traveling in the + x direction generated by a variable source initially has a wavelength λ of 235 μm and a maximum electric field Emax in the + y direction of 3.30*10-3 V/m. If the period of the wave is then increased by a factor of 2.80, what is the equation of the resulting magnetic field component of the wave?

B = E/c = 14.04T₁ = 11 pT

Explanation:

We know c = E/B where E = maximum electric field = 3.30 * 10⁻³ V/m, B = maximum magnetic field and c = speed of light

B = E/c also c = fλ = λ/T where λ = wavelength = 235 μm = 235 * 10⁻⁶ m and T = period

c = λ₁/T₁ = λ₂/T₂ T₂ = 2.8T₁ where λ₁,λ₂ are the initial and final wavelengths and T₁, T₂ are the initial and final periods.

T₁ = λ₁/c = 235 * 10⁻⁶ m/3 * 10⁸ m/s = 7.833 * 10⁻¹³ s = 0.7833 ps

T₂ = 2.8T₁ = 2.8 * 7.833 * 10⁻¹³ s = 21.93 * 10⁻¹³ s = 2.193 ps

λ₁/T₁ = λ₂/2.8T₁

λ₂ = 2.8λ₁ = 2.8 * 235 μm = 658 μm

c = λ₂/T₂ = 2.8λ₁/2.8T₁ = λ₁/T₁, since the speed of light c is constant.

B = E/c = E/λ₁/T₁ = ET₁/λ₁

B = ET₁/λ₁ = 3.30 * 10⁻³ V/m * T₁/235 * 10⁻⁶ m = 14.04T₁ Tesla

B = 14.04 * 7.833 * 10⁻¹³ s = 10.99 * 10⁻¹² T ≅ 11 pT