What is the locus of a surface when Phi(φ) coordinate is constant in Cylindrical and Spherical coordinate system?

Assume that we are given with ϕ = while ρ and z coordinates can take any value.

So, just apply the definition of ϕ coordinate. It is the angle made by the vertical half plane containing the given point with +X.

So obviously, all the points which are present on the same vertical half plane, would have same ϕ coordinate i.e. ϕ = . In other words, locus of ϕ = will be the vertical half plane.

So, locus of **ϕ = constant is a vertical half plane** stuck to the Z – axis making an angle ϕ with the +X axis.