Spherical Definition and 1000 Threads

Homework Statement Find the pressure on a uniformly charged spherical conducting shell of Radius R and total charge Q. The answer is (Q^2) / (32*π*ε*R^4) I´m fine doing this using the derivative of the energy as the sphere grows to get the force. My question is: Why do I get twice the answer...

This problem is driving me mad suppose that we have a positive charge inside a non conducting spherical shell uniformly charged the charge is at a random place inside the shell but not in the center the textbook says the charge will feel no force from the charges of the shell and the...

The volume charge density of spherical shell varies as ρ=-kr.If we have to calculate electric filed using gauss's law, can we treat as E. dA as E(dA) as there is azimuthal symmitry Homework Equations The Attempt at a Solution

Hi everybody, I am trying to solve the following problem and I get stuck on the last question. I would appreciate a lot that someone helps me . Here is the problem: Let D be the region bounded from below by the cone z= the root of (x^2 + z^2), and from above by the paraboloid z = 2 – x^2 –...

Converting to Spherical Coordinates...then integrating? Am I doing this right? Homework Statement Consider the integral ∫∫∫(x2z + y2z + z3) dz dy dx, where the left-most integral is from -2 to 2, the second -√(4-x2) to √(4-x2) and the right-most integral is from 2-√(4-x2-y2) to...

Homework Statement Suppose a planet whose surface is spherical and the gravitational potential exterior to it is exactly -GM/r, like that of a point mass. Is it possible to know if the inner mass distribution is actually shperically symmetric? Can a non-spherical mass distribution produce...

Homework Statement Two conducting spheres of radii R1 and R2 are kept widely separated from each other. What are their individual capacitance? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series-parallel connections...

Q: Consider your own eyesight. Can you detect any indication of spherical aberration? If so, describe what you see. A: I understand spherical aberration is generated by spherical lenses or mirrors and causes light to spread, which results in a blurry image. My initial thought was yes, a...

Homework Statement where λ= thermal conductivity \dot{q}= dissipation rate per volume Homework Equations qx=-kA\frac{dT}{dx} The Attempt at a Solution I don't know where to start from to be honest, so any help would be greatly appreciated

Homework Statement http://img109.imageshack.us/img109/1065/87070684.png Homework Equations 1) L_{\pm}=\pm\hbar e^{\pm i \phi}(\frac{\partial}{\partial\theta}\pm i cot\theta \frac{\partial}{\partial\phi}) 2) L_{\pm}Y^m_l = \hbar\sqrt{(l \mp m)(l \pm m+1)}Y^{m \pm 1}_{l} 3)Answer...

Homework Statement Firstly sorry for my bad english,i have a one question for you(İ try it but i didn't solve it ) Homework Equations The Attempt at a Solution i know problem will be solved spherical coordinates but i don't know how i get angles (interval) theta and fi ...

Hi all, Suppose I have measured an antenna's nearfield pattern and have a set of data f(theta, phi), where theta and phi are spherical coordinates, at a distance r from the antenna (we'll assume that the antenna is a point source to make it easier). How would I go about transforming this data...

The normalization condition is: ∫|ψ|^{2}d^{3}r=1 In spherical coordinates: d^{3}r=r^{2}sinθdrdθd\phi Separating variables: ∫|ψ|^{2}r^{2}sinθdrdθd\phi=∫|R|^{2}r^{2}dr∫|Y|^{2}sinθdθd\phi=1 The next step is the part I don't understand. It says: ∫^{∞}_{0}|R|^{2}r^{2}dr=1 and...

Homework Statement Consider a particle in a 2nm sphere with infinite potential energy outside and zero potential energy inside the sphere. Calculate the energy of the following wavefunctions: 1s, 2p, 3d Homework Equations H(hat) = p(hat)^2/2m(sub zero) + V(r) V(r) = ∞ when r ≥ 2 nm...

Homework Statement Calculate volume of the solid region bounded by z = √(x^2 + Y^2) and the planes z = 1 and z =2 Homework Equations The Attempt at a Solution

Homework Statement Find the capacitance of an isolated ball-shaped conductor of radius R1 sorrounded by an adjacent concentric layer of dielectric with permitivity ε and outside radius R2. Homework Equations The Attempt at a Solution The official solution says something like...

Homework Statement Hi I have an expression on the form df(v, \theta, \phi) = v e^{-v^2/C}\cos(\theta)v^2\sin(\theta)\,dv\,d\theta\,d\phi and I am trying to write it in cylindrical coordinates. Note that θ runs from 0..π, v is a velocity and C a real constant. So I wish to write it in terms...

∅θ,θI've come across two distinct 'versions' of the spherical coordinates. Could someone tell me which is correct or if both are fine. Version 1: A spherical coordinate is (rho,θ,∅) x=rhocos(θ)sin(∅) ; y=rhosin(θ)sin(∅) ; z=rhocos(θ) Version 2: A...

Hello, I am trying to solve the following integral (limits from 0 to inf). ∫j_1(kr) dr where j_1 is the first order SPHERICAL Bessel function of the first kind, of argument (k*r). Unfortunately, I cannot find it in the tables, nor manage to solve it... Can anybody help? Thanks a lot! Any...

Homework Statement Calculate the flux of vector field F = -3r through sphere radius 5 at the origin. Homework Equations The Attempt at a Solution Since the orientation is always exactly opposite of the orientation of the surface, I expect a negative answer. Also, since they...

Reading through my electrodynamics textbook, I frequently get confused with the use of the del (nabla) operator. There is a whole list of vector identities with the del operator, but in some specific cases I cannot figure out what how the operation is exactly defined. Most of the problems...

The Green's functions for a 3d wave are like δ(r - ct)/r -- so if you have static source at the origin that is turned on at t=0, you get an expanding ball around it of radius ct, with strength 1/r. If you look just at the XY plane, you see an expanding disc of value 1/r. Similarly, if you...

Homework Statement http://img13.imageshack.us/img13/5793/84188411.jpg Homework Equations Find a condition on b such that x = 0 is a local minimum of the potential function. The Attempt at a Solution To find local minimum, potential function (V) of the system should be written. V...

Homework Statement Prove the complex amplitude reflectance of a spherical mirror is given as exp[-jk(x2+y2)/R] Homework Equations Transmittance of a spherical mirror is also exp[jk(x2+y2)/2f] The Attempt at a Solution I have totally no idea how to go about doing this. Can I just...

Homework Statement Given two concentric spherical metal shells, with radii a and b (a < b), and surface charge densities Sa and Sb. Find the capacitance if Sa = - Sb. Homework Equations C = Q/V The Attempt at a Solution I would know how to solve this if the absolute values of the...

So I've done some problems where a sphere intersects with a cylinder and I needed to find the volume of the intersected region using triple integrals. For example, if I needed to find the domain of integration for the intersection of the sphere $$x^2+y^2+z^2=a^2$$ and the cylinder...

Homework Statement The point is (0, -8, 0) r≥0 0≤θ≤2∏ 0≤\varphi≤∏ Homework Equations The Attempt at a Solution So here is what I've done so far: I know that r=8 because x and z are 0 I know that θ=∏/4 or 3∏/4, but which one? both of these satisfy the following equation...

Homework Statement Consider a solid sphere of radius r to be placed at the bottom of a spherical bowl radius R, after the ball is given a push it oscillates about the bottom. By using the Lagrangian approach find the period of oscillation.Homework Equations The Attempt at a Solution Ok so this...

Homework Statement The electric field of a spherical electromagnetic wave in vacuum can be written in the form of: E(r,θ,phi)= A(sin(θ)/r)*[cos(kr-ωt)-(1/kr)sin(kr-ωt)]phi Show that E is consistent with ALL of Maxwell's equations in vacuum and find the associated magnetic field...

Homework Statement A 2 meter deep swimming pool is filled with water. A mirror is placed at the bottom and a small fish swims 5 cm (0.05m) below the surface. If you look at the swimming pool from above, how deep does the fish appear to be (a), and how deep does it's image appear to be (b)...

Hey, I just wanted to double check if what I am thinking is correct. Say you have a spherical shell of inner radius R1, and outer radius R2, which is made of a perfect conductor carrying a charge q1. E=0 inside (r<R1) (and also between R1<r<R2 but not worried about that) So the...

I had a tutorial today and my tutor said these questions are very trivial so we can simply look at it at home. But after going home, I found that I don't know how to do Q 35. I know that p<3 is responsible for the big sphere with r=3. But I don't know why the other part is responsible for...

I want to check if I'm doing this problem correctly. Homework Statement Region bounded by x^2+y^2=4 and bounded by the surfaces z = 0, and z=\sqrt{9-x^2-y^2}. Set up triple integrals which represent the volume of the solid using spherical coordinates. Homework Equations...

Hey, If initially I have some solid sphere spinning at some initial angular velocity and in its final state I have the same solid sphere spinning at a different angular velocity except some of its mass has moved to a ring 45 degrees in latitude from centre , such that this ring of mass is...

i just need some help on how to start the process of proving it. suggestions/recommendations/anything will help!

Homework Statement How to determine the integral bounds of phi in spherical polar coordinates. Please see my exact question at the end of page 2 of 2 in attachments. Homework Equations Please see my attachments The Attempt at a Solution Please see my attachments.

I have two questions. I believe I have solved the first question and would like confirmation of this answer; the second question I'm a little bit lost on so any help there would be greatly appreciated! I am working on a problem set in which I must derive the equation for heat conduction in...

Homework Statement There is a perfectly absorbing spherical shell with radius R1 suspended in space. Inside is a smaller spherical shell with radius R2. Inside that shell is a ball of radius R3. All three objects are concentric. In the center of the ball is a point source radiation with power...

Homework Statement Two parallel plates are placed 0.10 m apart with one vertically above the other and their edges aligned. The potential difference of the upper plate is 100 kV relative to the lower plate. What charge must a spherical raindrop of diameter 1.0 mm carry if it remains...

Imagine an uncharged spherical conductor centered at the origin has a hole of some strange shape carved out inside it, and a charge q is placed somewhere within this hole. What is the field outside the sphere? Is it even possible to determine the electric field simply from the given...

Homework Statement Two spherical conductors are connected by a long conducting wire, and a charge of 10.2 Micro-coulombs is placed in the combination. One sphere has a radius of 5.99 cm and the other has a radius of 7.99cm. What is the electric field near the surface of the smaller sphere...

Homework Statement Compute the divergence of v = (1/(r^2)) r where r = sin(u)cos(v)i + sin(u)sin(v)j + cos(u)k, r^2 = x^2 + y^2 + z^2 The Attempt at a Solution I can only think to express r as a function of x,y,z and do it. I know there's a simpler way though, but it's driving me...

I'm wondering how the use of spherical shaped detectors causes pincushion distortion. I can understand the shape of the detector affecting the final image but I thought the lines would bend out as when a hemisphere is laid out flat, a point appearing near the center from the front on angle would...

What's the difference in the representation of spherical harmonics and the orbitals themselves? they look exactly the same to me... unlike the radial part of the wavefunction though.

We are doing rotational volume in Calculus II right now. I know the basic rules for the disk, washer, and shell methods, but I'm having trouble getting started with these questions. I'm not sure how to set up the equations. Any sort of help would be great. Thanks so much!

Picture of the problem: As seen by the diagram above, a2 < a1 But the spherical Pythagorean theorem states that cos c = (cos a)(cos b). The triangle can either have a1,b,c or a2,b,c as its sides, which means the above equation contradicts itself. Am I missing something? thanks.

So in the case of a spherical conductor, if we have charge distributed over it the electric field inside will ALWAYS be zero. Even when we place a charge near the sphere the field inside is zero right? And if we have a spherical insulator and we uniformly distribute the charge, the electric...

Homework Statement express a volume element dV= dx*dy*dz in spherical cooridnates.

I am having some difficulties understanding something here, it seems to me that the book at some point deny itself or I clearly do not get it. So it firstly states that: Inside the spherical shell the potential energy does not depend on radius from the center of the shell to the point of...

particles like protons and maybe photons, they are always spherical why? do they create a gravitational field?