Spherical Definition and 1000 Threads

Homework Statement A metallic spherical shell of radius a is cut in half at its equator. The two halves are separated very slightly and are maintained at potentials +V_{0} and -V_{0}. I am trying to find the electric field at the center of the sphere. Homework Equations The equation for...

Homework Statement The magnetic field around a long, straight wire carrying a steady current I is given in spherical coordinates by the expression \vec{B} = \frac{\mu_{o} I }{2∏ R} \hat{\phi} , where \mu_{o} is a constant and R is the perpendicular distance from the wire to...

Homework Statement (a) For spherical coordinates, show that \hat{\theta} points along the negative z-axis if \theta = 90°. (b) If \phi also equals 90°, in what direction are \hat{r} and \hat{\phi}?Homework Equations The Attempt at a Solution can i just explain this in words.. like for a...

Homework Statement The potential outside of a spherical conductor is given by V = keQ/r. Using Er = -dV/dr, derive the electric field outside this charge distribution. The Attempt at a Solution I attempted to take the negative derivative of V being -1/(r2) and then multiplying it...

Hi everyone! So we're learning about the Hydrogen atom in QM and I'm having trouble reconciling something in my head. We're looking at potentials that are only radius dependent, like the Coulomb potential. Now, I know the math. I see that we assume the wave function can be separated into the...

Homework Statement In order to advance on a problem I'm working, I need to covert this ellipsoid from cartesian to spherical coordinates. \frac{x^2}{a^2} +\frac{y^2}{b^2} +\frac{z^2}{c^2} = 1 Homework Equations x^2 +y^2+z^2= \rho ^2 x=\rho sin \phi cos \theta y= \rho sin \phi sin...

Homework Statement When an object is at distance u1 and u2 from pole of concave mirror, images of same size are formed. Find the focal length of the mirror. Homework Equations 1/v+1/u=1/f The Attempt at a Solution Can u please ray diagram for this question. I think their is only...

Should be quite easy, really, given that it's just adding things together, hey ho. Problem a position vector of point (1), identified by sherical coordinates, is 5m away from point (2). I have a unit vector R1,2 identified by spherical coordinates [Aex - Bey +Cez], giving the direction to...

Hello everyone, I recently tried to find the surface area of a hollow cone (there is no base, like an ice cream cone) using spherical coordinates. With cylindrical coordinates I was able to do this easily using the following integral: \int \int \frac{R}{h}z \sqrt{\frac{R^{2}}{h^{2}} + 1}...

1. Homework Statement [/b] Consider two thin, conducting, spherical shells as shown in cross-section in the figure below. http://capa.physics.mcmaster.ca/figures/sb/Graph25/sb-pic2565.png [b] The inner shell has a radius r1 = 17.2 cm and a charge of 10.3 nC. The outer shell has a radius r2 =...

Hello there, could anyone help me with a certain basic problem in relativistic QM? What would be the wave function of a photon (or generally a particle with zero rest mass) in a spherical 3D cavity, having potential energy V=0 within the cavity and V=k outside the sphere (k>0)? I have been...

the radii of the curvature of the spherical surfaces which is a lens of required focal length are not same. it forms image of an object. the surfaces of the lens facing the object and the image are interhanged. will the position of the image change?

Hello, What do Alfven waves look like? Say you have a spherical galaxy. What would the Alfven waves of the three lowest frequencies look like? I read that they are transverse waves but I can't visualize a spherical transverse wave. Thanks! :)

Homework Statement Prove that {Y_{L}^{M}\left ( 0,\varphi \right )=\left ( \frac{2L+1}{4\pi } \right )^{1/2}\delta _{M,0}Homework Equations Y_{L}^{M}\left ( \theta,\varphi \right )=\left ( \frac{(2L+1)(L-M)!}{4\pi(L+M)! } \right )^{1/2}P_{L}^{M}(cos\theta )e^{im\varphi } \int_{\varphi...

Homework Statement Consider a Wavefunction: \psi(x,y,z)=K(x+y+x^2-y^2)e^{-r/a} Find expectation value of L^{2} , L_{z}^{2}, L_{x}^{2}. Homework Equations The Attempt at a Solution The first step would be a rewriting a wavefunction in terms of spherical coordinates: \psi=Kr(\cos\phi \sin...

Homework Statement http://img28.imageshack.us/img28/7118/capturenbc.jpg Homework Equations x2 + y2 + z2 = p2 http://img684.imageshack.us/img684/3370/eq0006m.gif The Attempt at a Solution Using the relevant equations I converted the given equation to: ∫∫∫e(p3/2) * p2 *...

Hello i know how to derive the components of acceleration in other coordinates like spherical start here : http://up.iranblog.com/images/0mbwuclckbu51bxt8jfa.jpg and at last we have : http://up.iranblog.com/images/geotowiaxdya2s6ewxk.jpg also , i know that acceleration is a contravariant...

Me and my friend have been arguing about the coordinate system used for the earth... specifically gravity. he's trying to tell me the value of gravity is -9.8ms/2, when I've read from several books and other online resources that's it 9.8ms/2... a positive number. Hes keeps going on and on and...

Homework Statement I'm trying to do problem 3.28 in griffith's electrodynamics. The problem statement is, to find the dipole moment of a spherical shell with charge distribution σ = kcosθ The way I tried to do it was to use the definition of dipole moment, which griffith defines as P=...

Homework Statement Here is the question given: Homework Equations The Attempt at a Solution So i set p as x^2 + y^2 + z^2 so p lies in between b and a. But how do i find the restrictions on the two angles, theta and phi?

I am trying to get a good grasp of the relation between the curl of a vector field and the exterior derivative of a 1-form field. In cartesian coordinates for flat R^3 the relationship is misleadingly simple. However, it still requires us to make an identification of the 2-form basis dx \wedge...

[b]1. Find the work done by the force F=r3*cos2\varphi*sin\varphi*\hat{r} + r3*cos\varphi*cos(2\varphi) \hat{\varphi} from the point (0,0,0) to (2,0,0) Homework Equations Work=\int F*dr where dr= dr\hat{r} + rd\varphi\hat{\varphi}The Attempt at a Solution When muliplying the line element, dr...

Homework Statement A thin spherical shell lying on a rough horizontal floor is hit by a cue in such a way that the line of action of force passes through the centre of the shell.as a result the shell starts moving with a linear speed v without any initial angular velocity.find the linear speed...

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}...

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 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 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...

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...