Spherical Definition and 1000 Threads

The correct one is 2nd, but why not first? Please guide , or tell me any link that relate to this derivation. Thanks

Hi Say I have a point on a unit sphere, given by the spherical coordinate $(r=1, \theta, \phi)$. Is this point equivalent to the point that one can obtain by $(x,y,z)=(1,0,0)$ around the $y$-axis by an angle $\pi/2-\theta$ and around the $z$-axis by the angle $\phi$? I'm not sure this is...

Shalom We are used to hearing that Coulomb's law doesn't settle with the relativity principle that nothing moves faster than the speed of light, in the sense that it embeds 'Action in a Distance'. Meaning that if somthing changes in r1 at time t1, and we write the law for any t before...

I'm studying Shankar's book (2nd edition), and I came across his equation (15.3.11) about spherical tensor operators: [J_\pm, T_k^q]=\pm \hbar\sqrt{(k\mp q)(k\pm q+1)}T_k^{q\pm 1} I tried to derive this using his hint from Ex 15.3.2, but the result I got doesn't have the overall \pm sign on the...

Homework Statement The question is about page 198 of Jackson's Classical Electrodynamics. The magnetic scalar potential is set to be: Phi = ∫ (dΩ' cosθ'/ |x-x'|). Using the spherical harmonics expansion of 1/|x-x'|, the book claims that only l=1 survives. I...

So, I'm to show that in spherical coordinates, the length of a given path on a sphere of radius R is given by: L= R\int_{\theta_1}^{\theta_2} \sqrt{1+\sin^2(\theta) \phi'^2(\theta)}d\theta, where it is assumed \phi(\theta), and start coordinates are (\theta_1,\phi_1) and (\theta_2, \phi_2)...

how the planets get in spherical shape if the they are formed by a big explosion ?

If I had a sphere centred at the origin with x > 0, y > 0 and z > 0 Would the angle boundaries be: 0 < θ < pi/2 0 < α < pi/2 ?

Is there an exact solution for the spherical symmetric collaps of pressureless dust? Can one see a Schwarzschild solution for r > Rdust with shrinking Rdust(t) ?

I'm currently working out the Schrödinger equation for a proton in a constant magnetic field for a research project, and while computing the Hamiltonian I came across this expression: (\vec{A}\cdot\nabla)\Psi where \Psi is a scalar function of r, theta, and phi. How do you evaluate this...

Homework Statement Find VR_{z}^{2} = \int \!\!\! \int \!\!\! \int_{E} (x^{2} + y^{2})dV given a constant density lying above upper half of x^{2}+y^{2} = 3z^{2} and below x^{2}+y^{2}+z^{2} = 4z.Homework Equations The Attempt at a Solution Why does it say upper half of x^{2}+y^{2} = 3z^{2}? It's...

Hello Can anyone tell me how the absorption of a polystyrene nanoparticles scales as a function of its diameter. The particle is spherical and it is placed in vacuum. A reference to a paper I can read would be nice. At this point I only want to know how the absorption scales not...

So I was pondering this question: On a conceptual level, how does a perfectly spherical helium balloon rise? I understand that the density of helium gas is lower than that of our atmospheric composition of gases, but that is not giving the full perspective for me. On a molecular level, I feel...

1. For a stationary plasma of electrical conductivity 1.00 x108 Ω-1 m-1 estimate the time taken for a magnetic field to permeate a spherical volume of 3.0 m radius. I have been looking at the question for some time now and I am struggling with where to begin. Any help would be much appreciated.

Hi, I'm a little confused about how to apply the real spherical harmonics when building a hydrogen wave function. I'm doing a computational project, so I want to work with a wave function which is strictly real, and I'm hoping I can do so by building the orbitals using the real spherical...

Homework Statement Convert the integral from rectangular coordinates to spherical coordinates 2 √(4-x^2) 4 ∫ ∫ ∫ x dz dy dx -2 -√(4-x^2) x^2+y^2 Homework Equations x=ρ sin∅ cosθ y=ρ sin∅ cosθ z=ρ cos∅ In case the above integrals cannot be understood: -2...

Homework Statement Homework Equations The Attempt at a Solution Working backwards I found that adding C1 (of radius a and b) and C2 (of radius b and c) in parallel gives the answer. Not sure why they can be modeled as capacitors in parallel though..

Homework Statement Consider the spherical well such that V(r<a) = -V0 and V(r≥a) = 0. Calculate the l = 0 partial wave scattering cross section in the low energy limit for this potential. Homework Equations σ = \frac{4 \pi}{k^2} * \Sigma (2l+1)*sin^2(\delta_l) The Attempt at a...

Homework Statement three concentric hollow conducting shells are there . inner most is given charge +q , outer most is given charge -q and middle one is earthed , then find charge appearing on all the surfaces ? Homework Equations v= k q / r , E=k q /r2 The Attempt at a Solution no...

Hello how can Convert Cartesian coordinates to spherical with shape? for clear my question i explain a way to convert my coordinates in different spherical. for example i use this diagram to convert Cartesian coordinates to Cylindrical(with image to axises) for example: now how can i do...

Homework Statement Use spherical cords to compute area of a disk, that's center at x,y=0, and z=4, having a radius of 3 Homework Equations I set up a triple ∫∫∫ (r^2* sin(theta)), running from phi =0 to 2pi, theta=0 to arcsin(3/5), r=5sin(theta) to 5. The Attempt at a Solution It doesn't...

Homework Statement (see attachment 1) Homework Equations The Attempt at a Solution (see attachment 2) As the gas is ideal and there is no gravity, the pressure is same throughout the cloud. In the thin sphere shown, the mass of the gas is ##dm=dV \cdot \rho(r)##. Let ##\mu## be...

I am pretty much satisfied with the example of a rotating shell example 5.11 pg 367 griffiths electrodynamics.on many ocassions he chooses cartesian coordinates before integration (see 5.10 too) , integrates and finds w×r along y direction .then he manipulates w×r, and writes it down in...

We can easily find from gauss's theorem(or otherwise) the field inside and outside a uniformly charged spherical shell.But i was wondering what would be the field on the surface of the shell.

Homework Statement A spherical ball of mass m and radius r rolls without slipping on a rough concave surface of large radius R .It makes small oscillations about the lowest point.Find the time period. Ans : 2∏\sqrt\frac{7(R-r)}{5g} Homework Equations The Attempt at a Solution...

Suppose we have a hollow spherical shell made of a conducting metal, inside a slightly larger hollow spherical shell made of the same conducting metal. The shells are separated by a layer of insulation, so that the assembly is basically a spherical, hollow capacitor. If I cause the inner shell...

the calculation of the E field a distance z above a spherical surface of charge gives rise to this integral which can be done by partial fractions...I don't see this integral in Stewart's table did I not input correctly in Mathematica? Integrate [(z-R*u)/(R^2+z^2-2*z*R*u)^(3/2),{u,-1,1}]...

Homework Statement I am very confused about the differences between a conducting and nonconducting spherical shell. The biggest problem that I am having is the way that electric fields act both inside,outside, and within these shells. Any explanation would be much appreciated.

Homework Statement Evaluate the appropriate determinant to show that the Jacobian of the transformation from Cartesian (this is a typo, they mean spherical) pψθ-space to Cartesian xyz-space is ρ2sin(ψ).Homework Equations The Attempt at a Solution Uhm, I am lost. I'm supposed to prove that when...

Homework Statement A hollow spherical shell carries charge density \rho=\frac{k}{r^2} in the region a<=r<=b, where a is the inner radius and b is the outer radius. Find the electric field in the region a<r<b. I'm not allowed to use integral form of Gauss's law, must use differential...

Homework Statement I am currently trying to prove: S = ∫∫a2sinΦdΦdθ Here is my work (note that in my work I use dS instead of S, this is an accident): I end up with: S = ∫∫a*da2sinΦdΦdθ Where da is the infinitesimal thickness of the surface. Why am I getting the wrong answer?

Two thin lenses having focal lengths of +15 cm and -15 cm are positioned 60 cm apart. A bird stands 25 cm in front of of the converging lens. a. describe the image of the bird. Is it real or virtual? Upright or inverted? Magnified or reduced? b. If the bird is 10 cm in height, what is the...

Homework Statement Consider a point charge q > 0 which is surrounded by a hollow metal sphere (uncharged) with inner radius R1 and outer radius R2. Use Gauss Law to determine the electric field E=E(r)er in the following regions: (i) 0 < r < R1 (ii) R1 < r < R2 (iii) r > R2 Homework...

Hey, folks. I'm trying to derive the surface area of a sphere using only spherical coordinates—that is, starting from spherical coordinates and ending in spherical coordinates; I don't want to convert Cartesian coordinates to spherical ones or any such thing, I want to work geometrically...

Homework Statement Derive the expression for kinetic energy of a classical particle in spherical coordinates. Homework Equations I believe the answer I am supposed to reach is: T=\frac{1}{2} m (\dot{r}^2 + r^2\dot{\theta^2} + r^2\dot{\phi ^2}sin^2\theta) The Attempt at a Solution...

Homework Statement Two concentric spherical shells carrying uniformly distributed charges +Q and -Q at radii a and b, respectively (b>a). Now, they are immersed in a uniform magnetic field pointing along the z-axis. Find the angular momentum of the fields.Homework Equations No need. (I know...

Solving "poisson's equation" slowly rotating spherical shell of mass Homework Statement We have that \partial ^{\alpha}\partial _{\alpha}\bar{\gamma _{0\mu}} = -16\pi T_{0\mu} which is very similar to Poisson's equation if we treat each component of the metric tensor as a scalar field (the...

Homework Statement I do not have a specific question, I am just wondering how one would go about finding the capacitance of three concentric spherical shells. Suppose the outer radius of the each shell is a, b, and c from the center outwards. Homework Equations E= -gradV C = Q/ V...

How many grams of copper are required to make a hollow spherical shell having an inner radius of 5.70 cm and an outer radius of 5.75 cm? The density of copper is 8.92 g/cm^3. Ok, so, how do I find the height? Or solve the problem without the height?

Dear all, I am reading R.A. Sharipov's Quick Introduction to Tensor Analysis, and I am stuck on the following issue, on pages 38-39. The text is freely available here: http://arxiv.org/abs/math/0403252. If my understanding is correct, then the Jacobi matrices for the direct and inverse...

Homework Statement How do the charges distribute when I have a spherical conductor centered cavity with a point charge not in center inside the cavity? See image: Homework Equations N/AThe Attempt at a Solution I would guess solution 1, but my tutor says it's 4, and I just can't believe him...

Hi guys! I was wondering if anyone knew of a particularly nice book that taught one how to solve physics problems that need the use of green's functions and/or spherical harmonics. I can't seem to find a book that actually does this other than Jackson but I'd rather not tread there (I'm guessing...

Homework Statement A spherical pendulum consists of bob of mass m attached to a massless rod of fixed length R. The end of the rod opposite the bob pivots freely (in two directions) about some fixed point. For the conical pendulum (θ=constant) case, show that the conical angle is stable...

I have a uniform grid of data in spherical coordinates. e.g. theta = 0, 1, 2, ... 180 and phi = 0, 1, 2, ... 359 which forms a 2D matrix. I wish to rotate these points around a cartesian axis (x, y, z-axis) by some angle alpha. To accomplish this I currently do the following: 1. Convert to...

[b]1. Homework Statement -38.0 nC of charge is uniformly distributed throughout a spherical volume of radius 34.0 cm. How much charge is contained in a region of radius 23.0 cm concentric with the charge distribution? Homework Equations Charge density = λ/area The Attempt at a...

Homework Statement Prove the La Placian of V(x,y,z)=(zx^{2})/(x^{2}+y^{2}+z^{2}) in Cartesian coordinates is equal to that in Spherical coordinatesHomework Equations \nabla^{2}V=0 The Attempt at a Solution I have attempted to calculate all the terms out, and there were A LOT. I was hoping...

Hello! I need to find the force exerted by a sphere on an object, with the height of the object on the sphere and the object of the mass konwn. I need to find the reaction of the spherical surface on the object. Thanks!

Homework Statement Consider a hollow spherical conductor with total charge +5e. The outer and inner radii are a and b, respectively. (a) Calculate the charge on the sphere's inner and outer surfaces if a charge of -3e is placed at the center of the sphere. (Use the following as...

Homework Statement (see attachment) Homework Equations The Attempt at a Solution I don't quite understand the question. It asks the distance of the "unilluminated patch" from the cylinder. There will be only a single point where the rays will intersect. Rest everywhere, it is...

Homework Statement A spherical insulator of radius R and charge density ρ = ρo/r2 where r is the distance from its centre. Find the electric field at a point inside and outside the insulator. Homework Equations EA = Qencl/εo The Attempt at a Solution What's throwing me off is...