What is the locus of a surface when r coordinate is constant in Spherical coordinate system? - The Right Gate

# What is the locus of a surface when r coordinate is constant in Spherical coordinate system?

What is the locus of a surface when r coordinate is constant in Spherical coordinate system?

Consider r coordinate equal to 2 i.e. r = constant and no restrictions over the value of φ and θ coordinates. So, just apply the definition of r coordinate.

r is the distance of the point from origin. And all the points present on the sphere of radius, r = 2, will be lying at a distance of 2 from the origin. Of course phi and theta coordinates for such points are different. But they all have r coordinate as 2.
Hence, locus of r = 2 is a curved surface of the sphere centered at origin at having radius 2.

So, the locus of r = constant is a curved surface of the sphere centered at origin with radius equal to that r.

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