Spherical Definition and 1000 Threads

I've been trying to prove a rather simple looking concept. I have a code that calculates states of a 3D anisotropic oscillator in spherical coordinates. The spherical harmonics basis used to expand it's solutions in radial coordinate constraint the spectrum such that when the Hamiltonian is...

Homework Statement I'm feeling a bit ambivalent about my interpretation of spherical coordinates and I'd appreciate it if someone could clarify things for me! In particular, I'd like to know whether or not my derivation of the coordinates is legitimate. Homework Equations Considering...

Homework Statement A thick spherical shell with inner radius R and outer radius S has a uniform charge density d.(A) What is the total charge on the shell? Express your answer in terms of R, S, d, and π. (B) Express the electric field as a function of distance from the center of the sphere r...

Hi there. I've been looking around for a decent physical explanation of the differences in the phase relationships between acoustic pressure and particle velocity in different types of waves. Mathematical analyses abound, e.g...

Homework Statement What is the flux of r(vector) though a spherical surface of radius a? Homework Equations to solve this use spherical coordinates. The Attempt at a Solution ∫a . ds

Hey guys, I have a problem that is giving me trouble. Homework Statement I have to solve time dependent diffusion equation ##D\nabla^2 T(r,t)=\frac{\partial T}{\partial t}## (##D## is diffusion constant and ##T(r,t)## is temperature function) for a spherical shell of radii ##r_1## and ##r_2##...

New to the forum but stumbled upon this and thought it might be beneficial to query more scientifically minded individuals. I am a filmmaker and use a variety of lenses to acquire certain looks. One of which is anamorphic cinematography. (http://www.red.com/learn/red-101/anamorphic-lenses)...

Homework Statement As a part of my self study I am trying to find the covariant basis vectors in the spherical polar coordinates. Since I have never done anything like this before I would appreciate if someone could tell me whether I am on the rigth track. Homework Equations...

I am trying to solve the 'ant and honey problem on a spherical bowl' to find the shortest route between two points on a sphere when the path is constrained by not being allowed to pass higher than a certain latitude (so interrupting some great circles connecting the two points). I intuitively...

In considering the shortest paths between two points on a sphere I came across the following interesting problem: An ant sits on the outside of a glass bowl of spherical curvature (radius R), at a distance d from the lip of the bowl. It sees a drop of honey on the inside of the bowl directly...

Homework Statement If you have a spherical interface between two different "media" (like air and water), and an object is placed in the one with the lower index of refraction, with the interface being convex toward the object, how can you tell if the image will be real or virtual? Here's a...

Consider the region above the $z=-\sqrt{2-x^2-y^2}$ and below $z=-\sqrt{x^2+y^2}$. Let $x=r\sin\phi\cos\theta$, $y=r\sin\phi\sin\theta$, $z=r\cos\phi$ I want the range of the variables. I get $0\leq r\leq\sqrt{2}$. How do I work out the range of $\phi$ and $\theta$ ?

Homework Statement i am confused which eqaution to use for formula of refraction at spherical surface , do i need to put a modulus for n2-n1 ? some book gives modulus , while the other book not . which one is correct? Homework Equations The Attempt at a Solution

Homework Statement A semi-circle shaped cylindrical glass block has a radius of curvature of 10.0cm. and a refractive index of 1.50 as shown. A pin is placed at the centre of curvature O . How far from the surface do the pin appear to be when it is viewed along the axis of the spherical...

Hello, I was just after an explanation of how people get to this conclusion: Say you are looking at the Helmholtz equation in spherical co-ordinates. You use separation of variables, you solve for the polar and azimuthal components. Now you solve for the radial, you will find that...

Homework Statement Hi! This is not really a problem. I'm just confused on how to express the charge distribution of a set of point charges in spherical coordinates. From our discussion, ρ(\vec{r})=\sum\limits_{i=1}^N q_i δ(\vec{r}-\vec{r}') where \vec{r} is the position of the point where...

Homework Statement In spherical coordinates (ρ,θ,ø); I understood the ranges of ρ, and θ. But ø, still eludes my understanding. Why is ø only from 0 to π, why not 0 to 2π??

Hello, As a science writer, I've tasked myself with acquiring a thorough theoretical and historical understanding of Quantum Mechanics. It would be interesting to know if there has ever been any experimental verification of Laplace's spherical harmonics, relating to the quantum mechanical...

We are very used to see diagrams of atoms as being composed by little spheres each one with their own characteristics, such as mass, electrical charge, etc. I have also read and heard in many different scientific divulgation media about the scale of the nucleus’ dimension and the size of...

Hey guys, This is my first post here, so I will apologize in advance in case I'm posting this in the wrong section. I wrote a very simple function to calculate spherical harmonics in matla, and I used this function during 3 years. Yesterday I found that the function was actually wrong, and...

Homework Statement ##\iiint_W (x^2+y^2+z^2)^{5/2}## W is the ball ##x^2+y^2+z^2 \le 1## The Attempt at a Solution changing to spherical ##0 \le \theta \le 2\pi ; 0 \le \phi \le \pi ; 0 \le \rho \le 1## ##(x^2 + y^2 + z^2)^{5/2} \Rightarrow ((\rho \sin \phi \cos...

from wiki: Suppose we have a hemisphere of radius 10 r10 (a) and cut it in ten horizontal slices (1 is on the top), does that mean that all slices have the same surface ? even slice 1 has surface 62.8 (2\pi *10*1)? and its a (r1) =4.36? so, the area of slice 4 (like all others) is...

This isn't really a homework question, but may be similar to a typical example problem so I posted it here. Homework Statement I want to find the max and min dot product of a 3d vector and all points in a sphere constrained by angles in spherical coordinates. Homework Equations A point...

An uncharged spherical conducting shell surrounds charge -q at the center of the shell. Then a charge+ +3q is placed on the outside of the shell. When static equilibrium is reached, the charges on the inner and outer surfaces of the she are respecteively... +q,-q is the answer. Does the +3q...

Dear all, As I was reading my book. It said that the line element of a particular coordinate system (spherical) in R^{3} is so and so. Then it said that the metric is flat. I don't get how the metric is flat in spherical coordinate. Could someone shed some light on this please? Thanks

What is the use of spherical trigonometry besides in navigation. My math background consist of having n completed a course in calculus 1. Would I ever need to learn and understand spherical trigonometry for further math or physics? What do I gain learning it besides saying I know spherical...

I just derived the 3-D Cristoffel symbol of the 2nd kind for spherical coordinates. I don't think I made any careless mistakes, but once again, I just want to verify that I am correct and I can't find any place on line that will give me the components of the symbol so I can check myself. Here...

Homework Statement Find the electric field a distance z from the center of a spherical surface of radius R which carries a uniform density σ. Treat the case z<R (inside) as well as z>R (outside). Express the answers in terms of the total charge q on the sphere. Homework Equations E = \int...

I recently derived a matrix which I believe to be the metric tensor in spherical polar coordinates in 3-D. Here were the components of the tensor that I derived. I will show my work afterwards: g11 = sin2(ø) + cos2(θ) g12 = -rsin(θ)cos(θ) g13 = rsin(ø)cos(ø) g21 = -rsin(θ)cos(θ)...

i want to find V(t) At first i found this problem was very simple but when i try to write differential equations i ended up with these V' = kA that's for sure then i confined the problem only to spherical shape and no other shapes of raindrops involved as i can't express A in term of V alone(...

Homework Statement Three small spherical masses are located in a plane at the positions shown below. The masses are Q=0.700 kg, R=0.400 kg, and S=0.800 kg. Calculate the moment of inertia (of the 3 masses) with respect to an axis perpendicular to the xy plane and passing through x=0 and y=-3...

Homework Statement Hello.:smile: I need help to design a spherical vessel submarine with minimum mass which can withstand water pressure at depth of 8000 meter. It must satisfy this conditions: 1. vessel shall have minimum interval volume of 10m^3 2. outer diameter must less than 5m...

Homework Statement Consider a spherical cap, for which the surface area and volume is A(a,h) = \pi(a^2 +h^2) V(a,h) = \frac{\pi h}{6}(3a^2 +h^2) What would the aspect ratio dA/dV be? The Attempt at a Solution Clearly we would have dA = 2\pi a da + 2\pi h dh dV = \pi ha da +...

Homework Statement Sqrt(x^2+y^2)<=z<=x^2+y^2+z^2 With this problem I run into a few questions The first of which arises at the statement 1/2<=cos^2a Here I go about writing -1/sqrt(2)<=cosa<=1/sqrt(2) But when dealing with trigs it doesn't make any sense to write 3pi/4<=a<=pi/4 So...

As we know there are charge on spherical shell then electrical field inside the shell will be zero. 1) If there is no charge on the spherical shell, but has charge inside the shell then what is the electric field inside and outside the shell? 2) If there is charge on the spherical shell...

Homework Statement An object 0.6cm tall is placed 16.5cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 22.0cm. Determine the position, size, orientation and nature of the image. Homework Equations \frac {1}{S} + \frac {1}{S'} = \frac {1}{f} =...

Hi. http://www.nt.ntnu.no/users/jensoa/E-FY1006-31mai2012.pdf Please open the link and go to page 11, problem 3. It appears, after all, I understand nothing when it comes to the wave function of Hydrogen like atoms. So I kindly ask you to answer some questions I got: 1) "A selection of these...

Homework Statement We have two half-spherical electrodes, arranged so that they produce a spherically symmetric electric field. What is the magnitude of the electrical force on an electron between the two electrods? Specifications: Distance between electrodes: d=0.04 m Radius for first...

Homework Statement A conducting sphere of radius R has a charge Q. A particle carrying a charge q is placed a distance 2R from the sphere. Find the potential at point A located a distance R/2 from the center of the sphere on the line connecting the center of the sphere and particle q. Note...

If a spherical conducting shell is kept in an electric field (say, from a point charge kept at some distance outside the shell), will any charge be induced in the internal surface of the shell? Also what will the field be like inside the shell? Thanks.

Homework Statement Homework Equations ∫∫∫dV The Attempt at a Solution Ok so I started by setting my bounds equal to √(200-x^2-y^2) ≥ z ≥ √(x^2+y^2), √(100-x^2) ≥ y ≥ -√(100-x^2), 10 ≥ x ≥ -10 which I got from solving z^2 = (200-x^2-y^2) = x^2+y^2 => x^2+y^2 = 100 but it...

Hey pf! I was thinking about how div(curl(f)) = 0 for any vector field f. However, is this true for div and curl in spherical coordinates? It doesn't seem to be. If not, what needs to happen for this to be true in spherical coordinates?? Thanks all!

Homework Statement Write a triple integral in spherical coordinates that represents the volume of the part of the sphere X^2+Y^2+Z^2=16 that lies in the first octant(where x,y, and z are coordinates are all greater than or equal to zero) Homework Equations So i know this is in...

Hello, i don't know if my question is well posed, if i have a symmetric tensor Sij = (∂ixj + ∂jxi) / 2 with xi cartesian coordinates, how can i transform it in a spherical coordinates system (ρ,θ,\varphi)? (I need it for the calculus of shear stress tensor in spherical coordinate in fluid...

Homework Statement Homework Equations The Attempt at a Solution Is this the correct setup? \int^{\pi}_{\frac{3\pi}{4}}\int^{2\pi}_{0}\int^{\sqrt{2}}_{0}\frac{1}{\rho^{2}} rho^2 Sin\phi d\rho d\theta d\phi I gave up on itex. It was either that or my computer flying out the...

please tell me if i did this correctly: task: I'm trying to divide the differential dA by dV where.. dA = differential surface area of a sphere, dV = differential volume of a sphere dA=8\pirdr dV=4\pir2dr so then dA/dV= 2/r Also, if i treat this as a derivative, then would...

Consider two spherical hollow conductors, charged to Q1 and Q2 coulombs respectively. What happens when one is placed within the other, and they are connected by a thin metallic wire? I do know that if they were placed at a distance from each other, the charge is distributed in the ratio of the...

I am finding the electric field from a spherical shell at a point on the z-axis outside the shell. The shell is centered at the origin,and I am only allowed to use coulomb's law. I want to find dE in spherical coordinates first then transform it to Cartesian before integrating to get E. So I...

Homework Statement A conducting spherical shell has inner radius a, outer radius b, and has a +Q point charge at the center. A charge of -Q is put on the conductor. a) What is the charge on the inner and outer surface of the shell? b) What is the electric field everywhere? c) What...

Homework Statement A particle is confined to move on the surface of a circular cone with its axis on the vertical z axis, vertex at origin (pointing down), and half-angle α(alpha) a) write down the lagrangian in terms of spherical coordinates r and ø (phi) Homework Equations...