Spherical coordinates Definition and 351 Threads

I am always a little confuse in polar, cylindrical and spherical coordinates in vector calculus vs cylinderical and spherical coordinates in vector fields used in Electromagnetics. I want to clarify what my finding and feel free to correct me and add to it. A) Vector calculus: We use x =...

Hi, I'm modeling receptors moving along a cell surface that interact with proteins inside of a cell. I figured it would be easier to model the receptors in spherical coordinates, however I'm unsure of how to model a random walk. In cartesian coordinates, I basically model a step as: x = x +...

Homework Statement You know the p-slash operator in Cartesian coordinates: {p_{slash}} = {\gamma _\mu }{p^\mu } = {\gamma _0}{p_0} - \vec \gamma \bullet {\bf{\vec p}} ...but what is p-slash operator in spherical coordinates? Homework Equations - spherical coordinate transformation...

Homework Statement Let D be the region bounded below by the plane z=0, above by the sphere x^2+y^2+z^2=4, and on the sides by the cylinder x^2+y^2=1. Set up the triple integral in spherical coordinates that gives the volume of D using the order of integration dφdρdθ.Homework Equations The...

Homework Statement I am confused about spherical coordinates stuff. For example, we can parametrize a sphere of radius 3 by x = 3 sin \phi cos \theta y = 3 sin \phi sin \theta z = 3cos\phi where 0 \le \theta \le 2 \pi and 0 \le \phi \le \pi . I don't understand about the range...

Say I have a solid given using polar coordinates I want to compute its volume. We know that when switching from cartesian to polar, dV becomes \rho^{2}\sin\phi d\rho d\theta d\phi But I am not converting from cartesian to polar, I am already in polar coordinates. do I still have to...

I am stuck on this problem. Use these equations: \textbf{v}(\textbf{r}) = f(r)\textbf{r} \frac{\partial r}{\partial x} = \frac{x}{r} And the chain rule for differentiation, show that: (\nabla\cdot\textbf{v}) = 2f(r) + r\frac{df}{dr} (cylindrical coordinates) Any help greatly...

I looked at my notes, but they're either incomplete or I simply forgot what the professor did to derive the gradient in spherical coordinates. Once I know that, deriving the divergence and curl given the supplementary equations listed is fairly straightforward. It was a little easier but...

Homework Statement Evaluate \int\int\int 1/\sqrt{x^{2}+y^{2}+z^{2}+3} over boundary B, where B is the ball of radius 2 centered at the origin. Homework Equations Using spherical coordinates: x=psin\Phicos\Theta y=psin\Phisin\Theta z=pcos\Phi Integral limits: dp - [0,2] d\Phi -...

How do I find \nabla in Spherical Coordinates. Please help.

Homework Statement using spherical coordinates find the volume of the solid outside the cone z^2=x^2+y^2 and inside the sphere x^2+y^2+z^2=2 Homework Equations ρ=x+y+z ρ^2=x^2+y^2+z^2 dρdφdθ The Attempt at a Solution im lost

Homework Statement Use spherical coordinates to find the moment of inertia about the z-axis of a solid of uniform density bounded by the hemisphere \rho=cos\varphi, \pi/4\leq\varphi\leq\pi/2, and the cone \varphi=4. Homework Equations I_{z} = \int\int\int(x^{2}+y^{2})\rho(x, y, z) dV...

Hello, this one is doing my head in. I'm trying to plot and play with wavefunctions by moving the originm, but i need to do it in spherical coordinates. Suppose i have a function G(r',theta',phi'), centered at the origin of the system r',theta',phi'. I also have a similar...

Homework Statement Write the del operator in spherical coordinates? Homework Equations I wrote the spherical unit vectors: \hat{r}=sin\theta.cos\phi.\hat{x}+sin\theta.sin\phi.\hat{y}+cos\theta.\hat{z} \hat{\phi}=-sin\phi.\hat{x}+cos\phi.\hat{y}...

Homework Statement Inside the sphere x2 + y2 + z2 = R2 and between the planes z = \frac{R}{2} and z = R. Show in cylindrical and spherical coordinates. Homework Equations \iiint\limits_Gr\,dz\,dr\,d\theta \iiint\limits_G\rho^{2}sin\,\theta\,d\rho\,d\phi\,d\theta The Attempt at a...

Hi! I'm studying the selection rules and the spectrum of one-electron atoms. In the textbook it is said: "It is convenient to introduce the spherical components of the vector \epsilon which are given in terms of its Cartesian components by: \epsilon_1=-\frac{1}{\sqrt2}(\epsilon_x+i\epsilon_y)...

I want to evaluate the following integral: I(p_{1}, p_{2}, p_{3}) = \int \mathrm{d}^{4} q \mathrm{d}^{4}p \, \dfrac{1}{\left[ p_{2} + q \right]^{2} - i0} \dfrac{1}{\left[ p_{1} - q - p \right]^{2} + i0} \Theta(q^{0}) \delta(q^{2}) \Theta(-p_{2}^{0} -p_{3}^{0} - q^{0} -p^{0})...

there is a function \Psi =\frac{c}{\sqrt{r}}e^{\frac{-r}{b}} find the probaility in \frac{b}{2}<r<\frac{3b}{2}\\ region the rule states \int_{-\infty}^{+\infty}|\Psi|^2dv=1\\ 1=\int_{-\infty}^{+\infty}|\frac{c}{\sqrt{r}}e^{\frac{-r}{b}}|^2dv then they develop it as...

Homework Statement Given that: Write an equivalent integral in spherical coordinates. Homework Equations (Triple integral in spherical coordinates.) (Conversions from rectangular to spherical coordinates.)(What spherical coordinates entail) The Attempt at a Solution The region...

Here is a small screenshot of something I'm reading: http://img262.imageshack.us/img262/3585/sphericalcoords.png The first six equations are ok. (I don't think anyone actually needs the figure right? It's just general spherical coordinates). φ is the angle in the x-y plane. I get how the...

Find the volume of a tetrahedron under a plane with equation 3x + 2y + z = 6 and in the first octant. Use spherical coordinates only. The answer is six. x=psin(phi)cos(theta) y=psin(phi)sin(theta) z=pcos(phi) I've been trying to figure out the boundaries of this particular...

Homework Statement Let f(x,y,z) be a continuous function. To rewrite f(x,y,z) as a function of spherical coordinates, the conversion x-rcos(\theta), y=rsin(\theta), and z=rcos(\varphi). Suppose S is a region in 3 dimensions. How would you rewrite _{\int\int\int}s f(x,y,z)dV as the integral of a...

Hello people, I'm creating an algorithm on Matlab and need to find the distance between two points in spherical coordinates where I have (r1,theta1,phi1) for the first point and (r2,theta2,phi2) for the second point. Of course, since I'm programming, I shouldn't use the dummy Cartesian...

I can't muster my mind around this. Can you actually plot this vector on a graph at the point? The vector only specifies a length with no direction.

If you consider the vector function (expressed in cylindrical coordinates) \frac{1}{\rho} \hat{\phi} where \rho = \sqrt{x^2+y^2}, you notice it has a singularity at the origin ONLY. But if you express this in spherical coordinates, what you get is \frac{1}{r\sin \theta} \hat{\phi}, which is...

Homework Statement Hi. I have a simple question. Is it true that \frac{\partial r}{\partial x} = (\frac{\partial x}{\partial r})^{-1} ? Because I'm having some trouble with the conversion between rectangular and spherical coordinates. Homework Equations x = r cos \phi sin \theta...

Hi everyone! There's a question bothering me about the two coordinate systems - cylindrical and spherical: Consider the two systems, i.e. (r, \theta, \phi)\rightarrow\left(\begin{array}{c}r\sin\theta\cos\phi\\r\sin\theta\sin\phi\\r\cos\theta\end{array}\right) and...

Hi. I have this integral \int_0^{2\pi}\int_0^\pi \mathbf A\cdot\hat r d\theta d\phi where \hat r is the position unit vector in spherical coordinates and \mathbf A is a constant vector. Is it possible to evaluate this integral without calculating the dot product explicitly, i.e. without...

Homework Statement Identify surface whose equation in spherical coordinates is given p = sin(theta)*sin(fi) The Attempt at a Solution I know that y = r*sin(theta)*sin(fi). and thus, y = rp. This yields y = (x2 + y2)0.5*(x2 + y2+z2)0.5 However, this is rather ugly. The answer is...

Homework Statement Using Spherical coordinates, find the volume of the solid enclosed by the sphere x^2 + y^2 + z^2 = 4a^2 and the planes z = 0 and z = a. Homework Equations I have the solutions to this problem, and it is done by integrating two parts: V = V_{R=const.} + V_{z = const.} The...

Does anyone know a good sight that explains, step-by-step, how to derive unit vectors in spherical coordinates? I am at that unfortunate place where I have been looking at it for so long I know the answer from sheer memorization, but don't understand the derivation. From the definitions I am...

Homework Statement Find the surface area of the portion of the sphere x^2 + y^2 + z^2 = 3c^2 within the paraboloid 2cz = x^2 + y^2 using spherical coordinates. (c is a constant)Homework Equations The Attempt at a Solution I converted all the x's to \rho sin\phi cos\theta, y's to \rho sin\phi...

Hey all, I'm having trouble calculating a "workspace" volume. The volume is easiest modeled by using spherical co-ordinates, and is defined by these boundaries: (assume variables r, theta, phi) \rho: 1 to 1.1 meters \theta: 0.05 radians \phi: 0.1 radians Here's how I've set up my...

I have to proove something in QM but I'm stuck on a bit of math. Say I have two vectors: \vec{a} = (r_a,\theta_a,\phi_a) and \vec{b} = (r_b,\theta_b,\phi_b) What is the cosine of the angle between them? If my proof is to work the cosine of the angle between them have to be...

Hey guys, Im trying to figure out how the angles for the following sphere are obtained. x^{2} + y^{2} + z^{2} = 4, y = x, y = \sqrt[]{3}x, z = 0 I understand that the integral is: \int_{0}^{\pi/2}\int_{\pi/4}^{?}\int_{0}^{2} However, I can't not see how the "?" interval is...

After converting a surface over the region that \rho=sin\phicos\theta/a + sin\phisin\theta/b + cos\phi/c I also have that this region is equal to 1. I can't seem to get anywhere..

Hi everyone, I am REALLY confused and lost on where about to begin a conversion of a rectangular iterated integral to a spherical iterated integral. Can someone kind of guide me through on what to do first? Like for example, I drew the initial iterated integral in both 2d and 3d...

Homework Statement The outermost integral is: -2 to 2, dx The middle integral is: -sqrt(4-x^2) to sqrt(4-x^2), dy The inner most integral is: x^+y^2 to 4, dz The attempt at a solution Drawing the dydx in a simple 2d (xy) plane, it is circular with a radius of 2. So...

Hey all, I really need some clarification here. I've seen problems dealing with the Angular Momentum of a particle, working in spherical coordinates. Wolfram says that there is no simple way to perform this and do the determinant, and you will find many people and other websites claiming...

Find the volume of the portion of cone z^2 = x^2 + y^2 bounded by the planes z = 1 and z = 2 using spherical coordinates I am having trouble coming up with the limits Relevant equations dV = r^2*sin(theta)*dr*d(theta)*d(phi) r = sqrt(x^2+y^2+z^2) the problem is actually 2...

I'm doing a question on a 3D isotropic harmonic oscillator. At one point I need to find write the radial component of del^2. Lecturer has written \frac{1}{r^{2}} \frac{d}{dr} \left( r^{2} \frac{d}{dr} \right) where the del^2 used to be in the set of equations...

I'm doing a question on a 3D isotropic harmonic oscillator. At one point I need to find write the radial component of del^2. The lecturer has written 1/r^2 * d/dr * (r^2 * d/dr) I don't understand cause it looks like he hasn't actually changed anything, r^2 over r^2 ?

Homework Statement Use spherical coordinates to find the volume of the solid bounded above by the sphere with radius 4 and below by the cone z=(x^2 + y^2)^(1/2).Homework Equations All general spherical conversions Cone should be \phi=\pi/4The Attempt at a Solution So far I think the triple...

Homework Statement A system's wave function has the form \psi(r, \theta, \phi) = f(t, \theta)cos\phi With what probability will measurement of L_z yield the value m = 1? Homework Equations L_z|\ell, m> = m|\ell, m> The Attempt at a Solution I feel like there may be a typo...

Homework Statement Use Spherical Coordinates. Let H be a solid hemisphere of radius a whose density at any point is proportional to its distance from the center of the base. a) Find the mass of H. b) Find the center of mass of H. Homework Equations M=\int\int_D\int\delta dV...

Homework Statement A satellite is in motion over the Earth. The Earth is modeled as a sphere of radius R that rotates with constant angular velocity "\Omega" in the direction of Ez, where Ez, lies in the direction from the center of the Earth to the North Pole of the Earth at point N. The...

Homework Statement A solid lies above the cone z=\sqrt{x^2+z^2} and below the sphere x^2+y^2+z^2=z. Describe the solid in terms of inequalities involving spherical coordinates.Homework Equations In spherical coordinates, x=\rho\sin\phi\cos\theta, y=\rho\sin\phi\sin\theta, and z=\rho\cos\phiThe...

Homework Statement I'm doing a problem that involves expressing, for two arbitrary vectors \vec{x} and \vec{x'}, |\vec{x}-\vec{x'}| in spherical coordinates (\rho,\theta,\phi). Homework Equations Law of Cosines: c^{2}=a^{2}+b^{2}-2ab\cos\gamma where \gamma is the angle between a and b...

I don't think so since it's not a sphere (disk). I have not learned about cylindrical coordinates and Cartesian is just a pain, so I am assuming I am supposed to use polar or something. Can someone clear up my confusion? \int\int\int_E y\,dV where E lies above the plane z=0, under the plane...

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...