Question

Now consider a different electromagnetic wave, also described by: Ex(z,t) = Eocos(kz - ω t + φ) In this equation, k = 2π/λ is the wavenumber and ω = 2π f is the angular frequency. In this case, though, assume φ = +30o and Eo = 1 kV/m. What is the value of Ex(z,t) when z/λ = 0.25 and ft = 0.125?

Answer 1

The value of Ex(z,t) is calculated by substituting the given parameters into the wave equation and performing the necessary trigonometric and unit conversions. The result gives the electric field value at the selected position and time.

Step-by-step explanation:

The question involves calculating the value of the electric field Ex(z,t) for an electromagnetic wave given by Ex(z,t) = Eo cos(kz - ωt + φ), where Eo is the amplitude (1 kV/m), φ is the phase constant (+30° in this case), and k and ω are the wavenumber and angular frequency respectively.

To find the value of Ex(z,t) when z/λ = 0.25 and ft = 0.125, we need to substitute these values into the given equation after converting them into the proper units to match the equation's variables (z and t). The wavenumber k is given by 2π/λ, and the angular frequency ω is given by 2πf. The phase constant φ needs to be converted from degrees to radians for correct calculation (30° = π/6 radians).

Substituting the given values into the equation, Ex(z,t) = (1000 V/m) cos(2π(0.25) - 2π(0.125) + π/6). This results in the electric field value at the specified z and t.

Answer 2

Step-by-step explanation:

Ex(z,t) = Eocos(kz - ω t + φ)

k = 2π/λ , ω = 2π f

φ = +30° , E₀ = 10³ V .

z/λ = 0.25 , ft = 0.125

Ex(z,t) = Eocos(2πz/λ - 2πf t + φ)

Putting the values given above

Ex(z,t) = 10³ cos ( 2π / 4 - 2π x .125 + 30⁰ )

= 1000cos (90⁰ - 45+30)

= 1000 cos 75

=258.8 V .