# Questions tagged [spherical-coordinates]

Questions on spherical coordinates, a three-dimensional coordinate system where a point is represented in terms of its distance from the origin, and its latitude and longitude angles (or complements thereof).

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### Tensor identity in orthogonal coordinate systems

In Riley, Hobson & Bence's "Mathematical methods for physics and engineering" third edition, in the chapter about tensors, one of the exercises involves finding the expression for the ...
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### Finding the bounds of a triple integral (spherical coordinates)

I'm currently learning how to calculate the volume of a 3D surface expressed in spherical coordinates using triple integrals. There was this exercice (from here) which asked me to find the volume of ...
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### 3D Sphericall Symmetric Analytical Convolution

I am trying to analytically convolve two spherically symmetric functions in 3D spherical coordinates, a 3D Gaussian and a "box" (really a radial step function). Numerical convolution yields ...
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I will post an image which believe it is essential to understand the question: See the image: Figure book Spherical coordinates $r, \theta, \phi$ are perfectly intuitive because the angles $\theta$ ...
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### Find the mass of the ice cream cone

The region looks like an ice cream cone. It is an upside-down circular cone attached to a slice of a sphere. I'm pretty sure the way you are "supposed" to solve it is with spherical ...
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### Convert the rectangular coordinates of the cone to cylindrical coords.

The height of the cone is $4$ and the radius is $2$ given by the inequality $0 \leq z \leq 4-2\sqrt{x^2 + y^2}$. From that information we can see we have the point $(1,0,2)$ and we can use this to ...
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### Normal unit vector of sphere with spherical unit vectors $\hat r$, $\hat \theta$ and $\hat \phi$

I'm trying to find the normal unit vector at each point of the sphere $x^2+y^2+z^2 = a^2$ using cartesian and spherical unit vectors, as shown below. I was able to get it using cartesian unit vectors. ...
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### Using spherical coordinates, is there an equation of a sphere not centered at the origin? If so what is it?

I am a high school teacher teaching Calculus for the first time actually, I am teaching Multivariable Calculus (Calculus 3). Its been a solid 15 years since I took Calculus 3. During a discussion of ...
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### Convert function from cartesian coordinates to cylindrical and spherical

Introduction I have a point charge of magnitude $-6Q_0$. This point charge is placed in the origin of an orthogonal coordinate system. The electric field at a arbitrary point $P=(x,y,z)$ caused by ...
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