What Is the Equation of a Sphere in Spherical Coordinates?

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SUMMARY

The equation of a sphere in spherical coordinates is defined as ρ = r, where ρ represents the radial distance from the origin and r is the radius of the sphere centered at the origin. The Cartesian equation for a sphere is x² + y² + z² = r². The discussion highlights confusion regarding the representation of vectors and constants in spherical coordinates, emphasizing that a vector cannot equal a scalar constant. The correct interpretation of spherical coordinates is crucial for accurate mathematical representation.

PREREQUISITES
  • Understanding of spherical coordinates and their representation
  • Familiarity with Cartesian coordinates and their equations
  • Basic knowledge of vector mathematics
  • Ability to differentiate between scalar and vector quantities
NEXT STEPS
  • Study the relationship between Cartesian and spherical coordinates in depth
  • Learn about vector calculus and its applications in physics
  • Explore the derivation of equations for various geometric shapes in different coordinate systems
  • Investigate the use of spherical coordinates in multivariable calculus
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Students and professionals in mathematics, physics, and engineering who require a solid understanding of geometric representations in different coordinate systems, particularly those working with spherical coordinates and vector analysis.

Philosophaie
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Looking for the equation in spherical coordinates and the spherical equation with the unit vectors:
Frr + FӨӨ + FØØ = constant

The equation is:

x^2 + y^2 + z^2 = r^2

is the equation for a sphere radius = r centered at the origin. What is the cartesian equation?

x*x + y*y + z*z = r ?

What is the sphere in spherical coordianates?

r*cosӨ*sinØ*r + r*sinӨ*sinØ /(r*sin)*Ө + r*cosØ/r*Ø = Constant ?

or

r*cosӨ*sinØ*r + sinӨ*Ө + cosØ*Ø =Constant ?
 
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Philosophaie said:
Looking for the equation in spherical coordinates and the spherical equation with the unit vectors:
Frr + FӨӨ + FØØ = constant

The equation is:

x^2 + y^2 + z^2 = r^2

is the equation for a sphere radius = r centered at the origin. What is the cartesian equation?

x*x + y*y + z*z = r ?
What you gave before WAS the Cartesian equation. I can't make any sense of the equation you give here because the left side of the equation is a vector while the right side is a number.

What is the sphere in spherical coordianates?

r*cosӨ*sinØ*r + r*sinӨ*sinØ /(r*sin)*Ө + r*cosØ/r*Ø = Constant ?

or

r*cosӨ*sinØ*r + sinӨ*Ө + cosØ*Ø =Constant ?
The equation of the sphere you gave before, with center at (0,0,0) and radius r, in spherical coordinates is, of course, \rho= r.
Again, your "vector equation" is setting a vector equal to a number.
 

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