Spherical Definition and 1000 Threads

Hello all, Guys in my textbook they state that on a point mass at point outside spherical shell of uniform density, the gravitational force is just as if the entire mass of the shell is concentrated at the Centre of shell. The text also states, the force of attraction due to a hollow...

I thought any two concentric conducting spheres of radii a and b such that a<b form a spherical parallel plate capacitor.But according to my book A spherical capacitor behaves as a parallel plate capacitor if it's spherical surfaces have large radii and are close to each other. 1)it's spherical...

I have a particle in a spherical well with the conditions that V(r) = 0 is r < a, and V(r) = V0 if r ≥ a. In this problem we are only considering the l=0 in the radial equation. After solving this I found that in the region 0<r<a, u(r)=Bsin(kr) (k=√2mE/hbar), and in the other region...

Homework Statement Homework Equations /The Attempt at a Solution[/B] I am trying to solve problem 2-13 from my textbook "Principles of Electrodynamics" (see image below). I believe that I should be solving the potential as \varphi(r,\theta) = \sum_{n=0}^\infty (A_n r^n +...

Edit: Forgot to type "stumped" at the end of the title 1. Homework Statement Instead of typing it out, a link to a scanned document of the problem is here: http://imgur.com/Be3jSLp. Homework Equations The equations to use are stated in the problem here: http://imgur.com/Be3jSLp The Attempt...

Homework Statement Homework EquationsThe Attempt at a Solutionhere is the setup for each, can someone check if they are correct before I evaluate the volume?

Hello, I am trying to find the magnetic field that accompanies a time dependent periodic electric field from Faraday's law. The question states that we should 'set to zero' a time dependent component of the magnetic field which is not determined by Faraday's law. I don't understand what is...

I have to evaluate $$\int^1_{-1} \int^{ \sqrt {1-x^2}}_{ - \sqrt {1-x^2}} \int^1_{-\sqrt{x^2+y^2}}dzdydx$$ using spherical coordinates. This is what I have come up with $$\int^1_{0} \int^{ 2\pi}_0 \int^{3\pi/4}_{0}r^2\sin\theta d\phi d\theta dr$$ by a combination of sketching and...

I am in need of a spherical geometry book.can some one suggest a good one?

Homework Statement S is the sphere of equation x2 + y2 + z2 = 10z and C the cone of equation z= sqrt(3*( x2 + y2)) . The axes are measured centimeters. R of sphere = 5 D = 10 Total height is 10 cm Illustrate the solid E bounded by the C cone and the sphere S and calculate its volume using the...

Homework Statement A spherical brass shell has an interior volume of 1.60 x 10-3m^3. Within this interior volume is a solid steel ball that has a volume of 0.70 x 10-3m^3. The space between the steel ball and the inner surface of the brass shell is filled completely with mercury. A small hole...

I just wanted to check that I am thinking about the coordinate transition correctly. The relativistic generalization of Euler's equation is (from Landau & Lifshitz vol. 6) ## hu^\nu \frac{\partial u_\mu}{\partial x^\nu} - \frac{\partial P}{\partial x^\mu} + u_\mu u^\nu \frac{\partial...

hello, I am studying spontaneous decay of an atom in spherical cavity - but I am not getting any good book on that can anyone help me in this regard. thanks wasi

I am studying spherical astronomy can some suggest good books on spherical geometry.

Homework Statement The vector field ##\vec B## is given in spherical coordinates ##\vec B(r,\theta,\phi ) = \frac{B_0a}{r\sin \theta}\left( \sin \theta \hat r + \cos \theta \hat \theta + \hat \phi \right)##. Determine the line integral integral of ##\vec B## along the curve ##C## with the...

Homework Statement Determine the conductivity of the insulator in a spherical capacitor filled with weakly conductive dielectric. Specific conductivity of the dielectric is λ, the dielectric permittivity ε. Ansver in book is ##\Lambda = \frac{4\pi\lambda}{\epsilon} \frac{R_1R_2}{R_1-R_2}##...

Homework Statement 2 concentric conducting spherical shells, with radii a and 2a, have charge +Q and -Q respectively. The space between the shells is filled with a linear dielectric with permittivity ε(r) = (ε0*a)/(1.5*a - 0.5*r), which varies with distance r. a) Use Gauss's law to determine...

Homework Statement Solve the Laplace equation inside a sphere, with the boundary condition: \begin{equation} u(3,\theta,\phi) = \sin(\theta) \cos(\theta)^2 \sin(\phi) \end{equation} Homework Equations \begin{equation} \sum^{\infty}_{l=0} \sum^{m}_{m=0} (A_lr^l + B_lr^{-l -1})P_l^m(\cos...

Hi all, I'm having some problems in grasping/properly understanding the usage of the del operator ( ##\nabla## ) in spherical co-ordinates, and I was wondering if someone could point me to some good resources on the subject, or take a bit of time to try to explain it to me. It just doesn't seem...

Homework Statement I'm doing a question that requires me to take the dot product of 2 vectors in spherical coordinates. Both vectors have only an r component, can I just multiply the r components? Homework EquationsThe Attempt at a Solution

Homework Statement Find the volume of the solid region that lies inside the cone φ= pi/6 and inside the sphere ρ=4. Use rectangular coordinates. Homework Equations x=ρ sinφ cos θ y=ρsinφ sin θ z=ρ cos φ ρ^2=x^2+y^2+z^2 x= r cos θ y= r sin θ r^2=x^2+y^2The Attempt at a Solution at first...

Homework Statement Maybe I missed it, but in my notes and also in documents like (http://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_09.pdf) (equation 1.64), I see $$ \vec{r}\cdot\vec{p} = -i\hbar r \frac{\partial}{\partial r} $$ Where ##r## is...

Homework Statement Find the moment of inertia of a spherical shell (hollow) with mass M and radius R. Homework Equations ## I = \int r^2 dm ## The Attempt at a Solution This is method I use to find Moment of Inertia of solid sphere: We use circular cross sections. At some radius r...

Homework Statement I'm suppose to verify the given Laplace in (a) Cartesian (b) Sperical and (c) Cylindrical coordinates. (a) was easy enough but I need to know if I'm doing (b) and (c) correctly. I don't need a solution, I simply need to know if the my Spherical formula is correct, my...

Homework Statement Find the vector directed from (10,3π/4,π/6) to (5, π/4,π), where the endpoints are given in spherical coordinates. Ans -9.660ax, - 3ay. + 10.61az Homework Equations az=rCosΦ The Attempt at a Solution az=10Cos(π/6) +5Cos(π) =13.6 My answer differs. Where did i go wrong?

Greetings, I want to ask if there is any subroutine for computing a global spherical harmonic reference field. I read journal and they say it exists, I hope we can share information regarding this subject. Thank you in advance.

Homework Statement Two grounded spherical conducting shells of radii a and b (a < b) are arranged concentrically. The space between the shells carries a charge density ρ(r) = kr^2. What are the equations for the potential in each region of space?Homework Equations Poisson's and LaPlace's in...

In a spherical symmetric problem the only nonzero components of the electric and the magnetic field are Er and Br Why?

Hi, I am interested to see how to use the vector dot product formula in spherical coordinate system, $$ V_1= r + \theta, at (1,0,0)$$ and $$ V_2= r - \theta, at (1, \frac{\pi}{2}, \frac{\pi}{2})$$ how to evaluate their dot product? do I have to transfer them into cartesian system? what would...

I want to ask Is conducting shell same as uniformly charged thin spherical shell? Because while finding Electric field due to uniformly charged thin spherical shell surface charge density is taken the same happens in case of conducting/metallic shell all the charges reside on surface similarly...

Homework Statement Separate variables and integrate to find an expression for r(t), given r0 at t=0 Homework Equations M=ρ(4/3)πr3, thus V=(4/3)πr3 dM/dt=Cr3 where C is a constant The Attempt at a Solution ∫dM=∫Cr3dt M+constant=?? I have no idea how to integrate r because it's a...

Homework Statement This is really 3 questions in one but I figure it can be grouped together: 1. The vector A = i xy + j (2y-z2) + k xz. is in rectangular coordinates (bold i,j,k denote unit vectors). Transform the vector to spherical coordinates in the unit vector basis. 2. Transform the...

Homework Statement Show that the conduction and displacement currents cancel each other for a spherical radioactive solid emitting charged particles radially outwards Homework Equations Maxwell's equations Current density (j) Displacement current density (jd) The Attempt at a Solution I...

Homework Statement Homework Equations The path integral equation, Stokes Theorem, the curl The Attempt at a Solution [/B] sorry to put it in like this but it seemed easier than typing it all out. I have a couple of questions regarding this problem that I hope can be answered. First...

Homework Statement Translate the following equations from the given coordinate system into equations in each of the other two systems. Also, identify the surfaces so described by providing appropriate sketches. Homework EquationsThe Attempt at a Solution For my solutions, I obtained z=2r^2 for...

Homework Statement Sketch the solid whose spherical coordinates (ρ, φ, θ): 0≤ρ≤1, 0≤φ≤(pi/2) Homework EquationsThe Attempt at a Solution I was thinking that since ρ represented the distance from the point of the origin and φ represented the angle between the positive z-axis and the ray through...

1. Homework Statement Homework Equations Here we have to express ##\psi(\theta,\phi)## in terms of spherical harmonics ##Y_{lm}## to find the angular momentum. If ##\psi(\theta,\phi) = i \sqrt{\frac{3}{4\pi}} \sin{\theta} \sin{\phi} ##, it can be written as: $$ \frac{i}{\sqrt{2}} (Y_{1,1}-...

Homework Statement Given a spherical shell of radius R and the surface charge density ( being the angle from the top of the sphere and being a constant) find the electric potential and the electric field inside and outside the sphere. Check that both the potential is continuous inside and...

Homework Statement A charged spherical insulating shell has inner radius a and outer radius b. The charge density on the shell is ρ. What is the magnitude of the E-field at a distance r away from the center of the shell where r < a? Homework Equations Gauss' Law The Attempt at a Solution I...

I have the following integral: ## \oint_{S}^{ } f(\theta,\phi) \hat \phi \; ds ##Where s is a sphere of radius R.so ds = ##R^2 Sin(\theta) d\theta d\phi ## Where ds is a scalar surface element. If I was working in Cartesian Coordinates I know the unit vector can be pulled out of integral and...

Homework Statement The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. Assume that these protons are incident on the Earth’s atmosphere from all directions at a rate of 1366. protons per square meter per second. Assuming that the depth of Earth’s atmosphere...

Homework Statement Evaluate r(hat and overdot), θ(hat and overdot), φ(hat and overdot) in terms of (θ , Φ) and the time derivatives of the two remaining spherical polar coordinates. Your results should depend on the spherical polar unit vectors. Homework Equations ∂/∂t= The Attempt at a...

(Moderators note: moved from technical forums, does not use template) How would someone approach this problem? Find mass in kg of spherical planet if: -71.11% of surface is covered by oceans - avg depth of oceans is 12.83 furlongs -avg density of water is 1.030 g/mL -avg radius of planet is...

Hello people ! I have been studying Zettili's book of quantum mechanics and found that spherical harmonics are written <θφ|L,M>. Does this mean that |θφ> is a basis? What is more, is it complete and orthonormal basis in Hilbert? More evidence that it is a basis, in the photo i uploaded , in...

Homework Statement In a spherical chamber with volume V , which contains a gas with pressure p1, there is a surface that has a much more low temperature than the other surface temperature of the sphere surface( which is kept constant). Because of that the particles that hit the coresponding...

consider two concentric spheres, where inner radius is r and outer radius is r+delta. Assume space between the two spheres is mass of an amount to be solved for. Given the metric inside the sphere, assumed to be varying as implied by the Cosmic Background Radiation anisotropy (CBRa), can the...

Homework Statement Hi everyone. Here's my problem. I know that the volume element in spherical coordinate is ##dV=r^2\sin{\theta}drd\theta d\phi##. The problem is that when i have to compute an integral, sometimes is useful to write it like this: $$r^2d(-\cos{\theta})dr d\phi$$ because...

Homework Statement Two concentric conducting spherical shells produce a radially outward electric field of magnitude 49,000 N/C at a point 4.10 m from the center of the shells. The outer surface of the larger shell has a radius of 3.75 m. If the inner shell contains an excess charge of -5.30...

Hi all. I'm struggling with taking dot products between vectors in spherical coordinates. I just cannot figure out how to take the dot product between two arbitrary spherical-coordinate vectors ##\bf{v_1}## centered in ##(r_1,\theta_1,\phi_1)## and ##\bf{v_2}## centered in...

Homework Statement Find the mass of the solid bounded from above z = √(25 - x2-y2) and below from z = 4, if its density is δ = k(x^2 + y^2 + z^2)^(-1/2). Homework Equations m = ∫∫∫δdV The Attempt at a Solution The plane z = 4 is transformed into ρcosφ = 4, that is, ρ = 4secφ. And x^2 +...