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

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

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 = $60^o$ 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 = $60^o$. In other words, locus of ϕ = $60^o$ 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.

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