Spherical Definition and 1000 Threads

Homework Statement The polarizatiob charge on the surface of a spherical capacitor is -\sigma_e \cos(\theta), at a point whose radius vector from the centre makes an angle \theta witha given axis Oz. Prove that the field strength at the centre is \frac{\sigma_e}{3 \epsilon_0}, Homework...

(b]1. Homework Statement [/b] A spherical weather balloon has a radius of 1m when it is 1500m high. You observe that the radius increases at a rate of 2cm/min as it continues to rise. At what rate is the surface area increasing when the radius is 4m? Homework Equations I thought...

Homework Statement Homework Equations The Attempt at a Solution I'm trying to find the steady state solution to the heat equation for a system of spherical shells (looks like http://correlatingcancer.com/wp-content/uploads/2009/01/nanoshell-thumb.jpg" ) where heat generation Q occurs in...

consider this following triple integral 1/(x^2+y^2+z^2)dxdydz bounded above by sphere z=(9-x^2-y^2)^1/2 and below by the cone z=(x^2+y^2)^1/2 what i have done: z=Pcospi P^2=x^2+y^2+z^2 9=x^2+y^2+z^2 P=0 to 3 pi=0 to pi/4 theta=0 to 2pi is this the correct range?

Homework Statement A -5-nC point charge is located at the center of a conducting spherical shell. The shell has an inner radius of 2 m, an outer radius of 4 m, and a charge of +7 nC. (Let the radially outward direction be positive.) (a) What is the electric field at r = 1 m? (Indicate the...

I am an ameteur physicist (i actually have my degree in meteorology), and i have some questions about the EM properties of liquid metals or ferrous liquids when in spherical form. I understand if you are too busy or if i sound off, but if you do have the time to answer a few questions, it would...

Homework Statement I want to understand spherical harmonics. I want to really grok them deeply. I want to be able to visualize them and understand them. I'm the sort who can't take anything on faith, especially where quantum mechanics is concerned. So I want to understand angular...

Homework Statement The problem is on page 40 of this PDF: http://web.mit.edu/8.02t/www/802TEAL3D/visualizations/coursenotes/modules/guide05.pdf Find the capacitance of a spherical capacitor with 2 different homogeneous dielectrics arranged concentrically.The Attempt at a Solution In that...

Homework Statement Compute the electric field generated by a spherically symmetric charged sphere of radius R with charge density of \rho = kr^{2} Homework Equations \oint _S \vec{E} \cdot \vec{dA} = \frac{Q_{enclosed}}{\epsilon_0} The Attempt at a Solution I know that this question...

Does anyone remember the formula for the area of a spherical patch in terms of two angles? Obviously you parametrize the surface and do the surface integral but I'm a bit too lazy/busy right now. So does anyone just remember the result? By spherical patch I mean something like this: I want...

Im trying to use spherical trig to solve a problem In the standard method to compute the angles, I already have only the following four angles A, a, B, b but from these, how can I compute either C, or c? Thanks

Divergence and Curl in cylindrical and spherical co are: \nabla \cdot \vec E \;=\; \frac 1 r \frac {\partial r E_r}{\partial r} + \frac 1 r \frac {\partial E_{\phi}}{\partial \phi} + \frac {\partial E_z}{\partial z} \;=\; \frac 1 {R^2} \frac {\partial R^2 E_R}{\partial R} + \frac 1 {R\;sin...

Hi folks, I'm looking for a derivation of the following statement (formula 76) http://img845.imageshack.us/img845/1550/screenshot4op.png Do you know any reference, where I can find a bit more detailed description? I reckon, you can find it in Jackson's electrodynamic book, but I couldn't find...

On May 25, 2011, the journal Nature published an article stating that the electron was experimentally found to be extremely spherical. In Volume II, Chapter 5 of Feynman's Lectures on Physics, he states that the electric field of an electron has been experimentally determined to vary...

Homework Statement Give a physical explanation of why a spherically symmetric Ylm cannot describe the state of a system with non-zero angular momentum. Homework Equations The Attempt at a Solution I was thinking that if Ylm is spherically symmetric then the particle is equally...

hi everybody, i would appreciate it if someone could clarify the concept of spherical aberrations in the context of high NA objectives in which use lenses are used that are not exclusively of the spherical type. a common thing that you hear is that some objective is corrected for 0.17mm...

I want to graph this vector field -^r/r^2 but I don't know how to do. Any help would be appreciated.

Homework Statement Evaluate the following triple integral by switching it to spherical coordinates? The integrand is r dzdrdθ The limits for the inner integral are 0 to r The limits for the middle integral are 0 to 3 The limits for the outer integral are 0 to 2π Homework Equations...

1. The problem statement Consider an infinite spherical charge distribution with constant charge density. According to symmetry of the problem, I expect the electric field at any point to be zero. But if you construct a Gaussian sphere and apply Gauss theorem, it will give you some finite field...

Homework Statement Using spherical coordinares, find the smaller volume bounded by the cone z=r and the sphere z^2+y^2+x^2=4 Homework Equations x^2+y^2+z^2=4 ; rho=2, z=rhocosphi The Attempt at a Solution Shot in the dark: Tried function integrating (rho squared - rhocosphi)...

atomic orbitals, what i just know about them is they are the regions around the nucleus where the probability of finding an electron is high and that is OK with s orbital because it is spherical. but when an electron in p orbital spins the probability of finding an electron should spin...

I've read many times now that the electric field inside a spherical shell is zero and all explanations of that fact have been based on imo false interpretation of the gauss law. The law itself says no such thing, atleast not explicitly. It merely says that the flux is zero. The only thing i can...

Whyyyyyy??! Whhhhhy?!?

The question is: A spherical capacitor contains a solid spherical conductor of radius 0.5mm with a charge of 7.4 micro coulombs, surrounded by a dielectric material with er = 1.8 out to a radius of 1.2mm, then an outer spherical non-conducting shell, with variable charge per unit volume p = 5r...

Going to 3rd year:want to "spherical harmonic" I'm going on to my 3rd year in university, my professor recommended that i should learn spherical harmonic over the summer...he told me to wiki it but that turned out to be a mess for me.. i have take first year calculus for physicist, and 2nd year...

Homework Statement A hollow sherical conducting shell is suspended in air by an insulated string. The total charge on the conductor is -6 microCoulombs. If an additional point charge of +2 microCoulombs is placed in the hollow region inside the shell what is the total charge induced on the...

My understanding is that the EM field at r.t generated by a radiating source can be described as the amplitude of the EM fields at r, at time t. Is there a corresponding photon associated with that wave? A unit surface area at large r from the source will have less energy passing through it...

I need help on starting and solving this problem. See attachment for problem.

Can anyone show me how you get the curl in polar or spherical coordinates starting from the definitions in cartesian coordianates? I haven't been able to do this.

The problem: "A convex spherical mirror is 25 ft from the door of a convenience store. The clerk needs to see a 6 ft. person entering the store at least 3 inches tall in the mirror to identify them. What is the radius of the mirror?" d_obj = do = 25 ft = 300 inches h_img = hi = 3 inches...

Homework Statement consider now a system of two charges: a point charge q>0 located at the position (x,y,z)=(a,0,0) and a point charge -q/2 located at (-a,0,0).Show that the equipotential surface V=0, i.e. with the same potential than at infinity, is a spherical surface. Determine the centre...

Hello! My problem is that I want to find (\frac{\partial}{{\partial}x}, \frac{\partial}{{\partial}y}, \frac{\partial}{{\partial}z}) in spherical coordinates. The way I am thinking to do this is...

Hi, this may seem like something I should ask in the math forums but, as I came into this problem in atomic physics I'm confident that this is a question more appropriate here than in the math forums. So far I've been only able to find the common integral of a product of three spherical...

Homework Statement I have to construct 3, 3X3 matrices for Lz, Lx, Ly for the spherical harmonics Y(l,m) given l=1 and m = 1,0,-1 So I can determine the relevant harmonics for these values of l and m. I act with Lz on Y to get L Y(1,0) = 0 L Y(1,1) = hbar Y(1,1) L Y(1,-1) =...

Homework Statement Calculate the z-component of the centre of mass for a northern hemisphere of radius R with constant density \rho_0 > 0 using spherical coordinates (r,\theta, \varphi ) defined by: x(r,\theta, \varphi) = r\sin\theta\cos\varphi \;\;\;\;\;\;0 \leq r < \infty y(r,\theta...

Moved my question to Intro Physics. Mods feel free to delete.

Homework Statement Find the spherical coordinates of the point with rectangular coordinates (2√2, -2√2, -4√3) Homework Equations ? The Attempt at a Solution The textbook gives the answer as (8, -pi/4, 5pi/6) No idea how to get to this. Any help appreciated.

Homework Statement A hollow spherical iron shell floats almost completely submerged in water. The outer diameter is 66.0 cm, and the density of iron is 7.87 g/cm3. Find the inner diameter. Homework Equations Fb=MG 4/3pir^3=Vsphere The Attempt at a Solution Not sure where to...

I'm writing a function for Matlab and I'm trying to figure out how to apply a torque matrix in cartesian coordinates to an object in spherical coordinates. The short story is this: For interest's sake, a friend and I have written a function with creates a tree which random branch...

Homework Statement This is a two part problem: 3- A conducting spherical shell of radius 19 cm carries a net charge of −8.15 μC uniformly distributed on its surface. Find the electric field at points just outside the shell. (Take the radially outward direction to be positive.) Answer in...

Homework Statement evaluate the following triple integral in spherical coordinates:: INT(=B) = (x^2+y^2+z^2)^2 dz dy dx where the limits are: z = 0 to z = sqrt(1-x^2-y^2) y = 0 to z = sqrt(1-x^2) x = 0 to x = 1 Homework Equations The only thing I know for sure is how to set...

This is not a homework. Actual this is part of my own exercise on conversion where \vec A = \vec B \;X\; \vec C and I intentionally set up B and C so the \theta_B \hbox { and } \theta_C \;=\; 60^o \; respect to z-axis: \vec B_{(x,y,z)} = (2,4, 2\sqrt{(\frac 5 3)}) \;\;\hbox { and }\;\...

How exactly would I go about finding the components of h_{ab} of the linear vacuum field equations for the external gravitational field of a static, spherical body situated at x = y = z = 0 for all t? I assumed since x = y = z = 0 for all t all h_{ab},x and ,y and ,z terms vanish from the...

Hello again, I've got a question about a star in a hydrostatic equilibrium. How do I derive an equation of motion for a pertubation in the full momentum equation? I'm attaching my solution (my_solution.jpg) , but I'm not quite sure about it. The full exercise is attached as...

Homework Statement What is the electric field if r=a and r=b? Reference:http://www.youtube.com/watch?v=BcuQ2c_WrMc" 2:11 And what if the net charge is just -Q on the conductor instead of -3Q? Will the electric field at r>b be 0? Reference: Same video, 3:00-3:10 Homework Equations...

I've got a unit sphere sitting at the origin. This sphere is cut by an arbitrary plane. I'm looking to find the equation of the circle that results from the intersection in spherical coordinates. This is for a computer program I'm writing, and I've already set it up to approximate this by...

In our textbook, the equation for terminal velocity has been derived from Stokes' law and it comes down as follows, vt = (mg)/6(pi)(eta)r (r is the radius of the spherical body) then, by putting the value of 'm' from m=(rho)V [where V = 4/3 * (pi)r3] we get, vt = 2(rho)gr2 / 9...

Homework Statement This is a bit hard to describe without a decent picture (or a decent brain) but try to bare with me. Picture below shows two spheres, if the origin is at centre of A, and a line d joins the centre of the two spheres, how do I describe the position of a point r from each...

For r = 3, 0 < theta < pi/2, 0 < phi < pi/3, find the surface area of the sphere. The answer given is 9pi, but I can't seem to work it out. Below is my working: 2\int_{r=0}^{3}\int_{\phi=0}^{\frac{\pi}{3}}r\sin\theta dr d \phi + 2\int_{r=0}^{3}\int_{\theta=0}^{\frac{\pi}{2}}r dr d \theta +...

Homework Statement Using Fermat’s principle, derive the spherical mirror formula in paraxial approximation: \frac{1}{s_o} + \frac{1}{s_i} = \frac{-2}{R} where so and si are object and image distances, R is the radius of curvature of the sphere. Homework Equations As far as I know you...