Electromagnetic Waves Equation

Description:

Relation between different parameters of the wave when a wave is traveling is known as wave equation.

Electric field of the electromagnetic wave is as shown −

Amplitude is E₀

Velocity is V

Wavelength is λ

Frequency is 𝝑

To find the value of electric field at a particular location at a particular time, we have −

E_y = E₀ cos(kx - wt + Φ)

Where,

E_y = Electric field (y direction) at distance x and time t

E₀ = Maximum value of E→

k = 2 π/λ = Propagation constant

ω = Angular frequency = 2 π 𝜗

Here, E₀, k, w and Φ are constant while E_y, x, t are variable and related to each other.

Similarly magnetic field is given by −

B_z = B₀ cos(kx - wt + Φ)

Example

We are given an equation −

E_y = 200 cos(6.28x - 25t + π/6)

We compare the given equation by our standard equation −

E_y = E₀ cos(kx - wt + Φ)

So,

peak value of electric field = E₀ = 200

Angular frequency = ω = 25

As we know −

k = 2 π/λ

∴ 2 π/λ = 6.28

∴ Wavelength = λ = π/3.14 = 1 m

Velocity is given by −

V = ω/k

V = 25/6.28 = 3.98 ms^-1