Question

A uniform plane wave propagating in empty space has electric field:

E(x,z,t) = ŷ E₀eʲʷᵗe⁻ʲᵏ⁽ˣ⁺ᶻ⁾/√², k = w/c₀
Inserting E(x,z,t) into Maxwell's equations, work out an expression for the corresponding magnetic field H(x,z,t).

Answer 1

The corresponding magnetic field for the given electric field is H(x,z,t) = -ẑ(E₀eʲʷᵗe⁻ʲᵏ⁽ˣ⁺ᶻ⁾/√²).

Step-by-step explanation:

The given equation for the electric field of a uniform plane wave can be plugged into Maxwell's equations to determine the corresponding magnetic field. Using the equation E(x,z,t) = ŷ E₀eʲʷᵗe⁻ʲᵏ⁽ˣ⁺ᶻ⁾/√², we can find the magnetic field H(x,z,t) by using the relationship between the electric field and magnetic field in electromagnetic waves.

In the case of a uniform plane wave, the electric field and magnetic field are perpendicular to each other and to the direction of wave propagation. This means that the magnetic field will have the form: H(x,z,t) = -ẑ(E₀eʲʷᵗe⁻ʲᵏ⁽ˣ⁺ᶻ⁾/√²).

So, the corresponding magnetic field for the given electric field is H(x,z,t) = -ẑ(E₀eʲʷᵗe⁻ʲᵏ⁽ˣ⁺ᶻ⁾/√²).