Question

An antenna radiates an electric far-field given by

E(r)=e−ʲᵏʳ/4πrsin(θ)θ
Express this field in terms of its Cartesian components.

Answer 1

To express the electric field in terms of its Cartesian components, convert the given spherical coordinates to Cartesian coordinates.

Step-by-step explanation:

To express the electric field in terms of its Cartesian components, we need to convert the given spherical coordinates to Cartesian coordinates. The electric field in spherical coordinates is given by:

E(r)=e^(-jkr)/4πrsin(θ)θ

The Cartesian components of the electric field are:

Ex = E(r)sin(θ)cos(ϕ)

Ey = E(r)sin(θ)sin(ϕ)

Ez = E(r)cos(θ)

Substituting the given expression for the electric field in spherical coordinates, we get:

Ex = (e^(-jkr)/4πrsin(θ)θ)sin(θ)cos(ϕ)

Ey = (e^(-jkr)/4πrsin(θ)θ)sin(θ)sin(ϕ)

Ez = (e^(-jkr)/4πrsin(θ)θ)cos(θ)