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

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