What Is the Equation of a Sphere in Spherical Coordinates?

In summary: The only vector in the equation is (r, Ө, Ø) and it can't be set equal to a number.In summary, the conversation discusses the equation for a sphere in spherical coordinates and the corresponding cartesian equation. The equation for a sphere with radius r and centered at the origin is x^2 + y^2 + z^2 = r^2. The equation for a sphere in spherical coordinates is ρ = r and it cannot be set equal to a number as it is a vector.
  • #1
Philosophaie
462
0
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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  • #2
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, [itex]\rho= r[/itex].
Again, your "vector equation" is setting a vector equal to a number.
 

Related to What Is the Equation of a Sphere in Spherical Coordinates?

1. What are spherical coordinates?

Spherical coordinates are a system of coordinates used to locate points in three-dimensional space. They consist of a radius, an angle from the z-axis, and an angle from the x-axis.

2. How do spherical coordinates differ from Cartesian coordinates?

In Cartesian coordinates, points are located using three perpendicular axes (x, y, and z). In spherical coordinates, points are located using a radius, an angle from the z-axis, and an angle from the x-axis.

3. How is a sphere represented in spherical coordinates?

In spherical coordinates, a sphere is represented by a fixed radius and two angles (θ and φ). The radius represents the distance from the origin to the surface of the sphere, while θ represents the angle from the z-axis and φ represents the angle from the x-axis.

4. What is the equation for a sphere in spherical coordinates?

The equation for a sphere in spherical coordinates is r = a, where r is the radius and a is a constant value representing the radius of the sphere. This equation holds true for all values of θ and φ.

5. How are values converted between Cartesian and spherical coordinates?

To convert from Cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ), the following equations can be used:
r = √(x² + y² + z²)
θ = arctan(y/x)
φ = arccos(z/r)

To convert from spherical coordinates (r, θ, φ) to Cartesian coordinates (x, y, z), the following equations can be used:
x = r*sin(φ)*cos(θ)
y = r*sin(φ)*sin(θ)
z = r*cos(φ)

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