Spherical Definition and 1000 Threads

Say I have {S_{x}=\frac{1}{\sqrt{2}}\left(\begin{array}{ccc} 0 & 1 & 0\\ 1 & 0 & 1\\ 0 & 1 & 0\\ \end{array}\right)} Right now, this spin operator is in the Cartesian basis. I want to transform it into the spherical basis. Since, {\vec{S}} acts like a vector I think that I only need to...

Homework Statement An insulator is in the shape of a spherical shell. The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = + 9 C (1 C = 10-6 C). You may assume that the charge is distributed uniformly throughout the volume of the...

at what value of k should the following integral function peak when plotted against k? I_{\ell}(k,k_{i}) \propto k_{i}\int^{\infty}_{0}yj_{\ell}(k_{i}y)dy\int^{y}_{0}\frac{y-x}{x}j_{\ell}(kx)\frac{dx}{k^{2}} This doesn't look like any orthogonality relationship that I know, it's a 2D...

Homework Statement What is the sum of the angles of a spherical triangle formed on the surface of a sphere of radius R? The triangle is formed by the intersections of the arcs of great circles. Let A be the area of the surface of the sphere enclosed by the triangle. This question is a...

First, I'd like to say I apologize if my formatting is off! I am trying to figure out how to do all of this on here, so please bear with me! So I was watching this video on spherical coordinates via a rotation matrix: and in the end, he gets: x = \rho * sin(\theta) * sin(\phi) y = \rho*...

Homework Statement Let ρ(r)= Qr/πR4 be the charge density distribution for a solid sphere of radius R and total charge Q.For a point 'P' inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is ? A) 0 B) Q/4πε°(r1)2 C) Q(r1)2/4πε°R4 D)...

Hi. I'm trying to proof the image formation property of a concave spherical mirror. I know you can do this easily with a particular choice of rays (namely one that hits the vertex and one that passes through the center of the sphere) but I would like to show that a generic ray yields the same...

Homework Statement Consider the process of blowing up a spherical balloon. Measurements indicate that the “surface tension” of the balloon material is ##k## (assumed constant here with units of force per unit length). Assuming that an air compressor used to blow up the balloon can deliver a...

Let's say we have r=R( theta, phi, t) on the surface of the particle and need to find the normal vector in Spherical Coordinate system. We know that, the unit vector =grad(r-R( theta, phi, t)) / |grad((r-R( theta, phi, t))| where grad is Spherical gradient operator in term of e_r, e_\theta...

Homework Statement Hi everybody! I would like to clear up some doubts I have about my electromagnetism homework: A positive point charge ##q## is placed in the center of an ideal conducting electrically neutral spherical shell, as shown in the attached picture. a) Calculate the electrical...

Homework Statement A spherical fruit has a radius of 1 inch. A slice has surface area of its peel equal to pi/8 . Determine the angle of cut for the slice. Homework Equations I'm sure there is a relevant equation here but I don't know it :-( The Attempt at a Solution So the radius is 1 inch...

Homework Statement Use spherical coordinates to find the volume of the solid enclosed between the spheres $$x^2+y^2+z^2=4$$ and $$x^2+y^2+z^2=4z$$ Homework Equations $$z=\rho cos\phi$$ $$\rho^2=x^2+y^2+z^2$$ $$dxdydz = \rho^2sin\phi d\rho d\phi d\theta$$ The Attempt at a Solution The first...

I am asked to find the total gravitational energy of a hollow sphere using the fact that the field energy density is given by ##u_g = \frac{-1}{8\pi G}g^2##. Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give...

Hey PF! I'm going through a textbook right now and it just said "obviously, you can't have an equilateral pentagon with 4 right angles in spherical geometry (Lambert quadrilaterals). However, I am not able to make the connection. can somebody help me understand why this is?

Homework Statement I am not sure whether to put this in the introductory level or advanced. It seems to be relatively introductory in an electromagnetism course. A spherical conductor of radius ##a## carries a charge ##q##. It is situated inside a concentric spherical conducting shell of...

Hi, I have to resample images taken from camera, whose target is a spherical object, onto a regular grid of 2 spherical coordinates: the polar and azimutal angles (θ, Φ). For best accuracy, I need to be aware of, and visualise, the "footprints" of the small angle differences onto the original...

where are the charge =0? please help...no idea how to do

Homework Statement A bowler throws a bowling ball of radius R = 11 cm along a lane. The ball (the figure) slides on the lane with initial speed vcom,0 = 7.8 m/s and initial angular speed ω0 = 0. The coefficient of kinetic friction between the ball and the lane is 0.13. The kinetic frictional...

I'm studing Gauss law for gravitational field flux for a mass that has spherical symmetry. Maybe it is an obvious question but what are exactly the propreties of a spherical simmetric body? Firstly does this imply that the body in question must be a sphere? Secondly is it correct to...

Homework Statement How much of the time are the proton and neutron in a deuteron outside the range of the strong force? Suppose the strong force can be described by a spherical potential with parameters ##V_0 = 35 MeV##, ##R = 2.1fm##. The binding energy for deuteron is ##E_b = 2.22 MeV## and...

Homework Statement A large number, N, of closely spaced turns of wire are wound in a single layer upon the surface of a wooden sphere of radius a. The planes of the sphere are perpendicular to the axis of the sphere (take axis to be horizontal), and turns are uniformly spaced per unit...

I was following this derivation of the solution to the Laplacian in spherical polars. I was wondering where the two equations ##\lambda_{1} + \lambda_{2} = -1## and ##\lambda_{1}\lambda_{2} = -\lambda## come from? Thanks.

Homework Statement The problem asks for a single triple integral (the integrand may be a sum but there must be a single definition for the bounds of the integral) representing the volume (in the first octant) of the shell defined by a sphere of radius 2 centered around the origin and a sphere...

Homework Statement transform the following vectors to spherical coordinates at the points given 10ax at P (x = -3 , y = 2, z=4) Homework Equations x y z can be chage into x = rsinθcosφ , y=rsinθsinφ , z=cosθ The Attempt at a Solution ax vector can be expressed ar,aθ,aφ so, I can change x ...

The problem is << transform the following vectors to spherical coordinates at the points given 10ax at P (x = -3 , y = 2, z=4)>> Actually, My first language isn't English, please understand that. x y z can be chage into x = rsinθcosφ , y=rsinθsinφ , z=cosθ ax vector can be expressed...

Homework Statement A spherical body of area A and emissivity 0.6 is kept inside a perfectly black body. Total heat radiated by the body at temperature T is (A) 0.4σAT4 (B) 0.8σAT4 (C) 0.6σAT4 (D) 1.0σAT4 Homework Equations Stefan-Boltzmann's Law: P = AεσT4The Attempt at a Solution If it wasn't...

Homework Statement A) [/B]Consider a hollow sphere of uniform density with an outer radius R and inner radius \alpha R, where 0\leq\alpha\leq1. Calculate its moment of inertia. B) Take the limit as \lim_{\alpha\to1} to determine the moment of inertia of a thin spherical shell. Homework...

Homework Statement Consider Minkowski space in the usual Cartesian coordinates ##x^{\mu}=(t,x,y,z)##. The line element is ##ds^{2}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}=-dt^{2}+dx^{2}+dy^{2}+dz^{2}## in these coordinates. Consider a new coordinate system ##x^{\mu'}## which differs from these...

1. The problem statemeent, all variables and given/known data The field electric's electromagnetic wave issued by a strut isotropic source is: \vec{E} = E_{0} r_{0}*cos(ωt − kr) \vec{θ} Find the magnetic field in spherical coordinates Homework Equations I think, i use the equation \vec{B} =...

I know that the limit for the spherical bessel function of the first kind when $x<<1$ is: j_{n}(x<<1)=\frac{x^n}{(2n+1)!} I can see this from the formula for $j_{n}(x)$ (taken from wolfram's webpage): j_{n}(x)=2^{n}x^{n}\sum_{k=0}^{\infty}\frac{(-1)^{n}(k+n)!}{k!(2k+2n+1)!}x^{2k} and...

Homework Statement By finding the Lagrangian and using the metric: \left(\begin{array}{cc}R^2&0\\0&R^2sin^2(\theta)\end{array}\right) show that: \theta (t)=arccos(\sqrt{1-\frac{A^2}{\omega^2}}cos(\omega t +\theta_o)) Homework EquationsThe Attempt at a Solution So I got the lagrangian to be...

Homework Statement A distant observer is at rest relative to a spherical mass and at a distance where the effects of gravity are negligible. The distant observer sends a photon radially towards the mass. At the distant observer, the photon's frequency is f. What is the momentum relative to...

Hello I've been having trouble finding the curl of A⃗ = r^2[e][/Φ]. Could someone help me please?

1. Calculate the work that must be done on charges brought from infinity to charge a spherical shell of radius R = 0.100 m to a total charge of Q = 125 μC.2. V = k_e\int{\frac{dq}{r}} \triangle V = - \int{E \cdot ds} W = q\triangle V 3. I started with assuming the spherical shell produces an...

Homework Statement Which is the angle between the ecliptic and the horizon in the moment that the point of Aries is hiding for an observer whose position is 18 degrees north? 2. Homework Equations None The Attempt at a Solution The first thing I have tried to is to do a drawing of the...

The following integral arises in the calculation of the new density of a non-uniform elastic medium under stress: ∫dx ρ(r,θ)δ(x+u(x)-x') where ρ is a known mass density and u = ru_r+θu_θ a known vector function of spherical coordinates (r,θ) (no azimuthal dependence). How should the Dirac...

Homework Statement An equation is given in spherical coordinates ## \rho sin(\phi) = 8cos(\theta) ## Express the equation in rectangular coordinates a) ## (x-4)^2 + y^2 = 16 ## b) ## x^2 + y^2 + z^2 = 16 ## c) ## x^2 + (y-4)^2 = 16 ## Homework Equations ## x = \rho sin \phi cos \theta, y...

how to calculate phase difference for spherical waves?how to say whether they are in phase or out of phase? in sinusoidal we can easily say whether they are in phase or out of phase just by looking at it,but how to do the same for spherical waves?

hi guys, i have a question. i saw this picture, and i don't really understand how they derived with the formula. The aim is basically to find the formula for the surface area of a spherical cap. why do you differentiate the x=sqrt(rˆ2-yˆ2)? how does that help to find the surface? and then...

Homework Statement A small tropical fish is at the center of a water-filled, spherical fish bowl 28.0 cm in diameter. (a) Find the apparent position and magnification of the fish to an observer outside the bowl. The effect of the thin walls of the bowl may be ignored. (b) Afriend advised the owner...

First, sorry if something is not totally clear, I'm translating physics term the best I can! 1. Homework Statement A sphere or radius a of permittivity ε2 is placed in a dielectric ε1. Without the sphere, we would have E = E0. We want to find the solution to this problem when ε2 = 1...

Hello people! I have ended up to this integral ##\int_{φ=0}^{2π} \int_{θ=0}^π \sin θ \ \cos θ~Y_{00}^*~Y_{00}~dθ \, dφ## while I was solving a problem. I know that in spherical coordinates when ##\vec r → -\vec r## : 1) The magnitude of ##\vec r## does not change : ##r' → r## 2) The angles...

Iam having trouble understanding how one arrives at the transformation matrix for spherical to rectangular coordinates. I understand till getting the (x,y,z) from (r,th ie., z = rcos@ y = rsin@sin# x = rsin@cos# Note: @ - theta (vertical angle) # - phi (horizontal angle) Please show me how...

Hello! The following wave solves the 3D wave equation: $$ \frac{\sin\left(k\sqrt{x^2+y^2+\frac{(z-vt)^2}{1-\frac{v^2}{c^2}}}\right)}{\sqrt{x^2+y^2+\frac{(z-vt)^2}{1-\frac{v^2}{c^2}}}}\cos\left(w\frac{t-\frac{vz}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}\right) $$ This is a propagating standing spherical...

Please explain in detail how to derive formula for capacitance of spherical capacitor?

I have a velocity vector as a function of a latitude and longitude on the surface of a sphere. Let us assume I have a point V(lambda, phi) where V is the velocity. The north pole of this sphere is rotated and I have a new north pole and I have a point V'(lambda, phi) in the new system. I have...

Hello guys, here's my question is how the book managed to solve this boundary value problem?? can anyone explain it to me in detail? thanks in advance.

Hello. I have a problem calculating the electric field from spherical charge distribution. The exercise is: 1. Homework Statement Homework Equations To solve the problem for $$ 0\le R < a$$ i tried 2 ways: $$ \vec{E} = \frac{\vec{a_R}}{4\pi\epsilon_0}\int_v\frac{1} {R^2}\rho dv $$ and the...

I am looking at this derivation of velocity in spherical polar coordinates and I am confused by the definition of r, theta and phi. http://www.usna.edu/Users/math/rmm/SphericalCoordinates.pdf I thought phi was the co latitude in the r,θ,∅ system and not the latitude. Of course the two are...

Homework Statement There are three point charges inside a conducting spherical shell of radius R. One of them of charge -2q is in the origin and the other two with charge q are in z=d and z=-d. Find the potential inside the sphere! Homework Equations ##\nabla^2\phi=4\pi \rho## 3. The attempt...