Question

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

Answer 1

Step-by-step explanation:

General equation of the electromagnetic wave:

`E(x, t)= E_0sin[(2\pi)/(\lambda)(x-ct)+\phi ]`

where

`\phi =` Phase angle, 0

c = speed of the electromagnetic wave, 3 × 10⁸

`\lambda =` wavelength of electromagnetic wave, 698 × 10⁻⁹m

E₀ = 3.5V/m

Electric field equation

`E(x, t)= 3.5sin[(2\pi)/(6.98*10^(-7))(x-3* 10^8t)]\\\\E(x, t)= 3.5sin[{9 * 10^6}(x-3* 10^8t)]\\\\E(x, t)= 3.5sin[{9 * 10^6x-2.7* 10^(15)t)]`

Magnetic field Equation

`B(x, t)= B_0sin[(2\pi)/(\lambda)(x-ct)+\phi ]`

Where B₀= E₀/c

`B_0 = (E_0)/(c) = (3.5)/(3*10^8)=1.2 * 10^(-8)T`

`B(x, t)= 1.2*10^(-8)sin[(2\pi)/(6.98*10^(-7))(x-3* 10^8t)]\\\\B(x, t)= 1.2*10^(-8)sin[{9 * 10^6}(x-3* 10^8t)]\\\\B(x, t)= 1.2*10^(-8)sin[{9 * 10^6x-2.7* 10^(15)t)]`