Spherical Definition and 1000 Threads

I recently read an article that said that experiments in synchotrons had indicated that an electron was the most spherical object in the universe. It stated that if an electron were the same diameter as the solar system, the variation in its diameter would be less than the thickness of a human...

Are spherical and cylindrical coordinate systems only a physical tool or is there some mathematical motivation behind them? I assume that they can be derived mathematically, but multivariable calculus texts introduce them and state their important properties without much background information...

Say we have a spherical shell of outer radius b and inner radius a. The shell has a total charge +3q and at it's center is a point charge of charge -q. I know that the E field for r>b would simply be: E = (3q-q)/(4πr^2ε0) and thus the electric potential inside the shell must be the same as the...

Homework Statement Evaluate the integral ∫∫dΩ V(Ω)Yml(Ω) for V(Ω) = +V0 for 0<θ<π/2 ; -V0 for π/2<θ<π Homework Equations I was hoping to apply the orthonormality properties of the spherical harmonics but this is a little more difficult since the integral breaks into two integrals over...

Homework Statement I want to derive the square of the total angular momentum as shown here: http://en.wikipedia.org/wiki/Angular_momentum_operator#Angular_momentum_computations_in_spherical_coordinates Homework Equations The x,y, and z components of angular momentum are shown in the...

Homework Statement a.) Set up the Lagrange Equations of motion in spherical coordinates, ρ,θ, \phi for a particle of mass m subject to a force whose spherical components are F_{\rho},F_{\theta},F_{\phi}. This is just the first part of the problem but the other parts do not seem so bad...

Homework Statement Find the electric field a distance z from the centre of spherical sphere of radius R which carries uniform density B. treat Z<R (inside) and Z>R (outside)………. By using law of cosine how to solve this problem? Homework Equations 1/4∏εo∫ (σ da/ r^2) cos(theta) The...

Homework Statement I am having so much trouble with this one problem ( and spherical coordinates in general ). Any help would be amazing: ∫∫∫ 1 / √(x2+y2+z2) Over -4≤x≤4, 0≤y≤√(16-x2), 0≤z≤√(16-x2-y2) Homework Equations The Attempt at a Solution I know that rho2 will...

Transformation from Cartesian to spherical polar coordinates In dimensions: x=r sinθ cos \varphi and y= r sin θ sin \varphi z=r cos θ Show one example of: ∂z\alpha/ ∂xμ . ∂xμ/ ∂z\alpha = δ\alpha\beta Now here is my answer: δyx=(∂y/∂r . ∂r/∂x) + (∂y/∂θ . ∂θ/∂x) + (∂y/∂\varphi...

Homework Statement I'm trying to solve I_l = \int^{\pi}_{0} d \theta \sin (\theta) (\sin (\theta))^{2l} Homework Equations the book suggest: I_l = \int^{+1}_{-1} du (1 - u^2)^l The Attempt at a Solution I think it's something related to Legendre polynomials P_l (u) =...

The setup: I am reading the review: arXiv:hep-th/0004098 (page 9-10). In Einstein-Maxwell theory, the gravitational field equations read: \begin{equation} R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} R = \kappa^2 \left( F_{\mu \rho} F^{\rho}_{\;\;\nu} - \frac{1}{4} g_{\mu \nu} F_{\rho \sigma}...

Hello, I'm trying to find a calculator or an equation that would help me determine the total electrical resistance between two points (A and B) on the surface of several concentric conductive spherical shells. The inputs for the calculation are the radii of the shells: r1, r2, r2, their...

Homework Statement Set up the triple integral for the volume of the given solid using spherical coordinates: The solid bounded below by the sphere ρ=6cosθ and above by the cone z=sqrt(x2+y2) Homework Equations The Attempt at a Solution I thought i had this set up right where ρ...

Dear Friends, I am trying to to find out if it is possible for the convex spherical lens to focus an ultraviot light to a single spot, and what is the power of the lens? Thank you very much for your help

Homework Statement Find the electric potential inside and outside a spherical capacitor, consisting of two hemispheres of radius 1 m. joined along the equator by a thin insulating strip, if the upper hemisphere is kept at 220 V and the lower hemisphere is grounded Homework Equations...

Homework Statement A fish is 10 cm from the front surface of a spherical fish bowl of radius 20 cm. (a) How far behind the surface of the bowl does the fish appear to someone viewing the fish from in front of the bowl? (b) By what distance does the fish’s apparent location change...

Homework Statement i just want to know how to visualize in spherical and cylindrical coordinates I am really having a rough time doing that for example why is that when we keep r constant we get a sphere and θ constant a cone why?? Homework Equations The Attempt at a Solution

Homework Statement A current I is flowing along the y-axis and a spherical surface with radius 1 m has its center at origin, as in the figure left. A closed contour C is chosen as in the figure, which is a boundary between two semi-sphere surfaces S1 and S2. Based on the...

Homework Statement Just need someone else to double check more work. I just want to know if I'm separating these variables correctly. Homework Equations \frac{\partial^2u}{\partial t^2} = c^2\nabla^2u The Attempt at a Solution Allow u(\rho, \theta, \phi, t) = T(t)\omega(\rho...

Homework Statement f(x,y,z) = 1 x^{2} + y^{2} + z^{2} ≤ 4z z ≥ \sqrt{x^2 + y^2} Homework Equations The Attempt at a Solution How can I know ρ if there is z variable? Do I just square root both 4 and z? For θ, since it is sphere it would be 0 ≤ θ ≤ 2\pi right? for \phi, is...

Homework Statement Using spherical coordinates, find the volume of the solid that lies within the sphere x2+y2+z2=4, above the xy-plane and below the cone z=√(x2+y2)Homework Equations The Attempt at a Solution This is what I have so far...

Hi, http://imageshack.us/photo/my-images/141/optica.png/ The sphere in the picture is made of glass with n = 1.60. The curved side of this sphere is a mirror. The question is why we see two images of the black dot. Homework Equations Snells law? The Attempt at a Solution One...

Hey all I'd like to help me.. thnx in advance here z tha Q's : 1) Two plane parallel conducting plates each have area S and are separated by a distance b. One carries a charge +Q ; the other carries a charge -Q. Neglect edge effects a) What is the charge per unit area on each plate ? where...

Homework Statement The question involves a triple integral, but I can figure that out once I know what this looks like visually. It is the graph of ρ = 1 + cos(∅) How exactly would I graph this? Homework Equations x = ρ * sin(∅) * cos(θ) y = \rho * sin(∅) * sin(θ) z = ρ * cos(∅)...

Homework Statement Verify by direct substitution in Laplace's equation that the functions (2.19) are harmonic in in appropriate domains in ℝ2 Homework Equations (2.19)= {u_n(r, \theta)= \lbrace{1,r^{n}cos(n \theta), r^{n}sin(n \theta), n= 1, 2...; log(r), r^{-n}cos(n \theta), r^{-n}sin(n...

Homework Statement Consider a simple spherical wave, with omega/k=c E(r, theta, phi, t)=((A sin theta)/r)(cos(kr - omega t) -(1/kr)sin(kr - omega t)) phi-hat i) Using Faraday's law, find the associated magnetic field B ii) Show that E obeys the remaining three of Maxwell's equations...

I didn't get any bites in the Calculus section a few days ago so I'm hoping since this is likely a pretty basic part of spherical harmonics that someone here can aid me. Also hoping reposting in a new section after a few days is allowed. Thank you in advance for your assistance! Homework...

Okay, so I'm working on using spherical harmonics to fit a model to some data. The thing is, everything can apparently be described as a "linear combination of spherical harmonics" but nobody is explaining in plain English what that means, at least to me! :D I see lots of double sum...

I'm having a hard time grasping the logical flow from orbital angular momentum to spherical harmonics. It feels like it's just sort of been sprung out of nowhere from both my lecture notes and the textbook. Can anyone help fill in the gaps that clearly must link them somehow? How did I get from...

Homework Statement Half the space between two concentric electrodes of a spherical capacitor is filled with uniform isotropic dielectric with permittivity ε. The charge of the capacitor is q. Find the magnitude of electric field strength between the electrodes as a function of distance r...

Homework Statement Convert the following integral to an equivalent integral in spherical coordinates. Do NOT evaluate the integral. ∫∫∫ r^3 dz dr dtheta limits of integration pi/4<theta<pi/2 0<r<2 0<z<√(2r-r^2) Homework Equations z=pcos(theta) r^2=x^2 +y^2 p^2=x^2 +y^2...

Homework Statement find the volume between the cone z=√(x^2+y^2), and the plane z=14+x, above the disk x^2+y^2≤1, for the exact number Homework Equations r^2=x^2+y^2; The Attempt at a Solution I found x=z, for x^2+y^2≤1, for solve r^2≤1, so r≤1, or r≥-1. for θ,from0 to 2pi, but I...

Homework Statement find the volume between the cone x=√y^2+z^2, and the spherex^2+y^2+z^2=196 Homework Equations The Attempt at a Solution for x=√y^2+z^2, I got x^2=y^2+z^2, and 2x^2=196, x=98, for this, I don't know what i am supposed to do then. Thanks!

Homework Statement the volume v=(4/3)(pie symbol 3.14..)r of a spherical balloon changes with the radius a)at what rate does the volume change with respect to radius when r= 2ft? b) by approximately how much does the volume increase when the radius changes from 2 to 2.2ft? Homework...

I've no idea where to put this question but here it is I am trying to work through the examples our lecture has given in class and I wasn't getting them at all the first thing that confused me was \nabla . \underline{r} = 3 I tried this myself with \nabla . \underline{r} =...

I'm doing a Lagrangian problem in spherical coordinates, and I was unsure how to express the kinetic energy, so I looked it up and wiki states it should be this: http://en.wikipedia.org/wiki/Lagrangian#In_the_spherical_coordinate_system Which would give me the correct answer, but I'm...

Homework Statement See figure attached. Homework Equations The Attempt at a Solution See figure attached for the provided solution. I got everything up to what I put in a red box. Where does he get that negative from? Did he do that with the intentions of reversing the...

We have a sphere that its center of mass is not located in its center. suppose it has a mass of m. what we want to do here is to write its movement equations, using Newton's laws or lagranigian.by move ment we mean writing the equations if a) a force F acts on the body on a surface that is...

Hey guys I am trying to understand a code for a Fortran 77 subroutine which calculates spherical harmonics using the CERN library RASLGF for legendre functions. The code looks like this subroutine harmonics(max,theta,phi,Yr,Yi) implicit none integer max,k,nn,n,grens...

I know that a spherical lens does indeed have spherical aberration, and I know that this is caused by the marginal and axel rays of light converging at different points. My question is why? What is it about the lens that makes the rays incedent on the edges of the lens focus at a closer point...

Homework Statement Given that Lz(x+iy)m=m\hbar(x+iy)m. Show that L+=(x+iy)m. 2. The attempt at a solution I'm probably grasping at straws here, but when I see the expression for Lz I instantly go to Lz|lm>=m\hbar|lm>. This then leads me to suspect that |lm>=(x+iy)m. Is this correct...

This is really a continuation from another thread but will start here from scratch. Consider the case of a static thin spherical mass shell - outer radius rb, inner radius ra, and (rb-ra)/ra<< 1, and with gravitational radius rs<< r(shell). According to majority opinion at least, in GR the...

For electrostatics, I know that conductors have 0 electric field inside. And I know that the surface of a spherical conductor has equipotential, (Maybe this is true for all shape of conductor in equilibrium right? ). So my question is, is the potential 0 inside a conductor as well? Is it...

In another thread I posed basically the folowing problem: Take the case of a stationary, non-rotating thin spherical shell of uniform area mass density - outer radius rb, inner radius ra, with (rb-ra)/ra << 1. There is consensus opinion that everywhere exterior and down to rb, spacetime is that...

I am facing some problem about derivatives in spherical coordinates in spherical coordinates: x=r sinθ cos\phi y=r sinθ sin\phi z=r cosθ and r=\sqrt{x^{2}+y^{2}+z^{2}} θ=tan^{-1}\frac{\sqrt{x^{2}+y{2}}}{z} \phi=tan^{-1}\frac{y}{x} \frac{\partial x}{\partial r}=sinθ cos\phi then \frac{\partial...

Homework Statement The following equation describes a surface in spherical coordinates. θ =pi/4 Write the equation in the cartesian coordinates? that is, (r,θ,Ø) to (x,y,z) Homework Equations x=rsinθcosØ y=rsinθsinØ z=rcosθ r=sqrt(x^2+y^2+z^2) θ=cos^-1(z/r) Ø=tan^-1(y/x) The...

Basically, BB ammos were shot from an airsoft gun into a water filled tank. The experiment was recorded using a video camera. I can calculate the approximate instantaneous velocity of the bullet under water at a given time using Logger Pro. 1. Relevant equations Drag force = 0.5 ρAC0v2 2...

In the attached picture is all of the information to complete this problem. The picture is of a solid sphere at the center of a hallow sphere, both of which are conductors. The question asks to find the total charge of the exterior and interior surfaces of the hollow conductor, as well as the...

Homework Statement A spherical conductor of radius a is surrounded by a spherical conducting shell of radius b, and the gap is filled with an insulating material of resistivity ρ. A thin wire connects the inner surface of the shell to the surface of the conductive sphere, and a potential of...

So I have the following shape for which I want to calculate the inertia matrix. Basically I just want to know what limits of integration I should use if I am using spherical coordinates. Assume the convention that phi is the angle from x to y in the xy plane and theta is from z to the xy plane...