Spherical Definition and 1000 Threads

Homework Statement R = 4000mi phi = 60 Me = 5.972E24 kg Mm = 5.972E16 kg distance of procession = 100 mi Homework Equations I know the answer is supposed to be ~1010 years. I also know what I am trying to do is have that e3 axis be pointing straight up, then when the mountain is placed on...

Hi I want to ask you if you know hot to write cos(theta)cos(phi) in terms of spherical harmonics? Thanks

After setting up Laplace's equation in spherical coordinates and separating the variables, it is not clear to me why the constants are put in the form of l(l+1) and why m runs from -l to l. Could anyone please help me ununderstand, or better yet, point me to a source that explains the entire...

Homework Statement So, probably a general question for most of all. It states that there is a charged insulating spherical shell with an inner radius of a/4 (a cavity) and an outer radius of a. The outer shell has a non-constant volume charge density of ρ=(-8α(r^2)). I need to find the electric...

Homework Statement a conducting spherical shell has radius R and potential V. If you want, you can consider it to be part of a capacitor with the other shell at infinity. you compress the shell down to zero size while always keeping it spherical,while a battery holds the potential constant at...

Homework Statement [/B] A thin spherical shell of radius R = 0.50 m and mass 15 kg rotates about the z-axis through its center and parallel to its axis. When the angular velocity is 5.0 rad/s, its angular momentum (in kg ⋅ m2/s) is approximately: a . 15 b. 9.0 c. 12 d. 19 e. 25 Homework...

Homework Statement Electric charge resides on a spherical surface of radius 0.3 centered at the origin with charge density specified in spherical polar coordinates by f(r,\phi, \theta) = 3 × 10^{-12} cos(\theta). Determine the total amount of electric charge on the sphere. Homework Equations...

Hi, I am going through the derivation of an instanton solution (n=1) in Srednicki Chp. 93. Specifically, I went through eqn.s 93.29-93.38. However the sign of the Levi-Civita Symbol is bugging me: It says that in 4D Euclidean space, \epsilon^{1234}=+1 in Cartesian coordinates implies...

Homework Statement Figure 23.52 gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by Es = 5.0 x 10e7 N/C. What is the charge on the sphere? Homework Equations Net Flux...

Now, this is kind of embarrassing, but I've been trying to do this for too long now and failed: I want to construct an atlas for ##S^2##, but I want to use spherical coordinates rather than stereographic projection. Of course the first chart image is simply ##\theta \in (0, \pi), \varphi \in...

Homework Statement I uploaded a file that gives the problem statement. Homework Equations I don't believe any equations are necessary. However, I could be wrong. I believe it to be a concept question. The relevant concept being that the electric field inside conducting materials in...

Homework Statement A spherical shell of mass M and radius R is completely filled with a frictionless fluid, also of mass M. It is released from rest, and then it rolls without slipping down an incline that makes an angle θ with the horizontal. What will be the acceleration of the shell down the...

Homework Statement Given two spherical conductors of radius R and tangent at O, both are charged and in equilibrium with surface charge density ρs=ρ0cos2theta. Calculate: a) Voltage of both spheres at O. (SOLUTION: V=2ρ0R/(3ε0) (...) Homework EquationsThe Attempt at a Solution So I tried to...

Homework Statement A Non-Uniform but spherically symmetric charge distribution has a charge density: \rho(r)=\rho_0(1-\frac{r}{R}) for r\le R \rho(r)=0 for r > R where \rho = \frac{3Q}{\pi R^3} is a positive constant Show that the total charge contained in this charge distribution is...

plane wave is represented as exp (ik.r) and the cylindrical wave as 1/sqrt(r) *exp(ik.r) and the spherical wave as 1/r*exp(ik.r) Have anyone tried to plot these waves? How to do it? Attempt: in Matlab assuming k=1 >> x=linspace(-1,1,100); >> for(ii=1:100) fp(ii)=exp(i*x(ii)); end >>...

hi guys, can someone please tell me how to find Theta and Phi from Yaw Pitch and Roll? I use my smartphone orientation sensor on a project and i need to calculate the smartphone's normal vector projection.

Homework Statement So I'm doing a question from one of my past exams as attached, there are no copy right issues with this document that I know of and have asked my lecturer who wrote the exam and he said I am welcome to upload it. The question is 1)b)iv), my attempt is attached. I end up with...

Homework Statement Well it is not the problem itself that bothers me but the maths behind a part of it. As part of finding the coefficient I had to solve the integral of (Sin(x))^(2l+ 1). The solution given by the solution manual just pretty much jumps to the final answer...

Homework Statement A solid sphere of mass M and radius R rotates freely in space with an angular velocity ω about a fixed diameter. A particle of mass m, initially at one pole, moves with constant velocity v along a great circle of the sphere. Show that, when the particle has reached the other...

Hello I have this problem - From a generator, I get a compton scattering with the electrons theta and phi angles. where I having the following equations for a particle px = E_particle * sin (theta) * cos (phi); py = E_particle * sin (theta) * sin (phi); pz = E_particle * cos (theta)...

Homework Statement The problem and its solution are attached as TheProblemAndSolution.jpg. Homework Equations V(D) = ∫∫∫_D ρ^2 sinθ dρ dϕ dθ The Attempt at a Solution How exactly does the solution get cos α = 1/√(3)? Also, when the solution goes from the step with two integrals to the step...

Homework Statement I have a PDE and I need to solve it in spherical domain: $$\frac{dF(r,t)}{dt}=\alpha \frac{1}{r^2} \frac{d}{dr} r^2 \frac{dF(r,t)}{dr} +g(r,t) $$ I have BC's: $$ \frac{dF}{dr} = 0, r =0$$ $$ \frac{dF}{dr} = 0, r =R$$ Homework Equations So, in spherical coord. First...

Homework Statement I have a PDE and I need to solve it in spherical domain: $$\frac{\partial F(r,t)}{\partial t}=\alpha \frac{1}{r^2} \frac{\partial}{\partial r} r^2 \frac{\partial F(r,t)}{\partial r} +g(r,t) $$ I have BC's: $$ \frac{\partial F}{\partial dr} = 0, r =0$$ $$ \frac{\partial...

Homework Statement There is a sphere of magnetic material in a uniform magnetic field \vec H_0=H_0\vec a_z, and after some calculations I got the magnetic moment vector \vec M_0=M_0\vec a_z, where M_0 is something that isn't important to my question. I am unsure if this magnetic moment vector...

Homework Statement A goldfish in a spherical fish bowl of radius R is at the level of the center of the bowl and at distance R/2 from the glass. What magnification of the fish is produced by the water of the bowl for a viewer looking along a line that includes the fish and the center, from the...

This is a long post. Sorry... 1. Homework Statement We are given a spherical capacitor with an inner conductor of radius ##a## and outer conductor of radius ##c##. The space between the conductors is half filled (##a<r<b##) with a dielectric with permittivity...

Homework Statement A spherical air bubble in a lake expands as it rises slowly to the surface. At the point it starts to rise, the pressure is 2.00 atm, the temperature of the water is 10.0 ∘C, and the radius of the bubble is 5.00 × 10^−3 m. At the surface, the pressure is 1.00 atm and the...

Can anyone please give an example of the use of bending disturbances in axisymmetrically loaded spherical shell using Geckeler approximation

Homework Statement Fig. below shows the cross-section of a porous spherical granule of radius a. The pores are initially saturated with water. The granule dries in air at pressure P and temperature T. The drying rate is controlled by diffusion of water vapor through the dry region B; the...

Homework Statement From Fick's Law of Diffusion, ##N_{A}C_{B} - N_{B}C_{A} = -DC \frac {dC_{A}}{dz}## Prove that Sh=2 for a volatile spherical droplet evaporating in a quiescent atmosphere. (Sherwood number for a sphere is given by ##Sh = \frac {k_{A}d}{D}##, where d = initial droplet...

Homework Statement The center of a 1.00 km diameter spherical pocket of oil is 1.00 km beneath the Earth's surface[/B]. Estimate by what percentage g directly above the pocket of oil would differ from the expected value of g for a uniform Earth? Assume the density of oil is 8.0*102 kg/m3...

Homework Statement The ground state wavefuntion of a system in spherical polar coordinates is given by: Ψ (r,θ, φ)= (A/r) [exp (-ar) - exp (-br)] where a, b, A are constants. i) Determine A as a function of a and b, so as to normalize the wavefuntion. ii) From Schrödinger equation find V (r)...

Homework Statement In this question, the Earth is modeled as a uniform sphere of radius 6400km. Objects are released from points just above the Earth's surface at the equator and at the North Pole. Which will fall to the Earth with the greater acceleration and by how much? Homework Equations...

Homework Statement Find the energy required to assemble two uniform hollow spheres of charge q between radii a and b with a volume charge density roh-v. The shells are separated by a distance c. *description of picture* - two identical spherical shells with inner radius a and outer radius b...

I'm trying to find the azimuthal angle unit vector \vec{\phi} in the cartesian basis by taking the cross product of the radial and \vec{z} unit vectors. \vec{z} \times \vec{r} = <0, 0, 1> \times <sin(\theta)cos(\phi), sin(\theta)sin(\phi), cos(\theta)> = <-sin(\theta)sin(\phi)...

I am accustomed to ##x=rcos(\theta)sin(\phi)## ##y=rsin(\theta)sin(\phi)## ##z=rcos(\phi)## ##-\pi<\theta<\pi##, ##-\pi/2 < \phi < \pi/2## but see some people using these instead ##x=rcos(\theta)cos(\phi)## ##y=rsin(\theta)cos(\phi)## ##z=rsin(\phi)## ##-\pi<\theta<\pi##, ##-\pi/2 < \phi <...

Homework Statement A spherical conducting shell of radius R is held at a potential V0. Outside the shell, the charge density is ρ(r) = ρ0sinθcosφ for R < r < 2R. Find the electrostatic potential everywhere outside the shell. Homework Equations Green's function in spherical coordinates between...

Homework Statement We are given a two concentric spherical shells with small radius ## a ## and larger radius ## b ##. The inner and outer shells are made of conducting material and there is a volume charge density, ##\rho\left(r\right) ##, that exists between the shells,. The boundary...

Homework Statement A thin spherical shell of radius R carries a surface charge density of the form kcos 3 θ . Find the electric field inside and outside the sphere and demonstrate explicitly that its components satisfy the relevant boundary conditions at the surface Homework Equations The...

Consider two frames: S and S', with S' moving to the right along the positive x-axis or S at a relative velocity v. The origins of S and S' coincide at t = 0. A spherical electromagnetic wave leaves the origin of S the moment S and S' coincide, or at t = 0. If we consider the transformation...

Homework Statement A thin spherical shell of radius R carries a surface charge density of the form kcos3 \theta Find the electric field inside and outside the sphere and demonstrate explicitly that its components satisfy the relevant boundary conditions at the surface. Homework Equations...

Homework Statement Homework Equations [/B] Surface area of sphere = 4*Pi*r^2, where r: is the radius of the sphere circleThe Attempt at a Solution Solution:[/B] 1. In terms of “r” and “R”, and the radius of sphere “S”, and “d”: Given that: · Surface area of both shaded area are equal...

1. Homework Statement Hi all, I am working through Gravity by James Hartle and have become stuck on a question asking me to calculate the area of a circle of radius r in the 2D geometry that is the surface of a sphere of radius a. A surface element on this sphere can be found to be...

Homework Statement A spherical conductor of radius ##a## carries a charge ##q## and also there is a jelly of constant charge density ##\rho## per unit volume extending from radius a out to radius ##b##. Find the electrostatic energy stored in the configuration. Homework Equations ##\oint...

Homework Statement A spherical charge distribution is given by p = p_0 (1- \frac{r^2}{a^2}), r\leq a and p = 0, r \gt a , where a is the radius of the sphere. Find the electric field intensity inside the charge distribution. Well I thought I found the answer until I looked at the back of...

Homework Statement Integrate $$\int_V \delta^3(\vec r)~ d\tau$$ over all of space by using V as a sphere of radius r centered at the origin, by having r go to infinity. Homework EquationsThe Attempt at a Solution This integral actually came up in a homework problem for my E&M class and I'm...

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.5cm , and the outer sphere has radius 15.5cm . A potential difference of 110V is applied to the capacitor. What is the energy density at r= 10.6cm , just outside the inner...

Hi All! the mathworld website http://mathworld.wolfram.com/SphericalSpiral.html claims that the loxodrome is given by the parametric equations ##x=cos(t) cos(c)## ##y=sin(t) cos(c)## ##z=-sin(c)## Why so? Now, as far as I can see, since the spherical coordinates are ##x=sin\phi cos\theta##...

Homework Statement Estimate the size of the spherical abberation of a spherical mirror of 1m-diameter and a focal length of 2 meter. (Hint: Calculate the size of the smeared image of a star at the focal point and compare it to the size (in arc-sec) of an extended object)Homework Equations The...

When transforming the Schrodinger equation into sphericall coordinates one usually substitutes psi(r,theta,phi) into the equation and ends up with something like this: -h(bar)^2/2m* d^2/dr^2*[rR(r)]+[V(r)+(l(l+1)*h(bar)^2)/2mr^2]*[rR(r)]=E[r R(r)] Question 1: How do I replace the Rnl(r) with...