Write equations for both the electric and magnetic fields for an electromagnetic wave in the red part of the visible spectrum that has a wavelength of 698 nm and a peak electric field magnitude of 3.5 V/m. (Use the following as necessary: t and x. Assume that E is in volts per meter, B is in teslas, t is in seconds, and x is in meters. Do not include units in your answer. Assume that E
Question
Answer:
Explanation:
General equation of the electromagnetic wave:
[tex]E(x, t)= E_0sin[\frac{2\pi}{\lambda}(x-ct)+\phi ][/tex]
where
[tex]\phi =[/tex] Phase angle, 0
c = speed of the electromagnetic wave, 3 × 10⁸
[tex]\lambda =[/tex] wavelength of electromagnetic wave, 698 × 10⁻⁹m
E₀ = 3.5V/m
Electric field equation
[tex]E(x, t)= 3.5sin[\frac{2\pi}{6.98\times10^{-7}}(x-3\times 10^8t)]\\\\E(x, t)= 3.5sin[{9 \times 10^6}(x-3\times 10^8t)]\\\\E(x, t)= 3.5sin[{9 \times 10^6x-2.7\times 10^{15}t)][/tex]
Magnetic field Equation
[tex]B(x, t)= B_0sin[\frac{2\pi}{\lambda}(x-ct)+\phi ][/tex]
Where B₀= E₀/c
[tex]B_0 = \frac{E_0}{c} = \frac{3.5}{3\times10^8}=1.2 \times 10^{-8}T[/tex]
[tex]B(x, t)= 1.2\times10^{-8}sin[\frac{2\pi}{6.98\times10^{-7}}(x-3\times 10^8t)]\\\\B(x, t)= 1.2\times10^{-8}sin[{9 \times 10^6}(x-3\times 10^8t)]\\\\B(x, t)= 1.2\times10^{-8}sin[{9 \times 10^6x-2.7\times 10^{15}t)][/tex]