Spherical Definition and 1000 Threads

My question is really about converting between spherical coordinates and cartesian coordinates. Suppose that ##\phi## and ##\theta## are defined as follows: ##\phi## is the angle between the position vector of a point and the ##z##-axis. ##\theta## is the angle between the projection of that...

Homework Statement I am trying to use the equation ##B_{dip} (r) = \nabla \times A## to find the magnetic field due to a dipole at the origin pointing in the z direction (where A is the magnetic vector potential). The correct answer should be: ##B_{dip} (r) = \frac{\mu_0 m}{4 \pi r^3} \ (2...

Part (a) is easy to do by setting up a triple integral, but for part (b), I was a bit confused by the diagram provided by the solutions manual: Why is the spherical wedge (shaded) graphed on the z-y axis? In the most general case, shouldn't the two lines that form angle $\phi_1$ and $\phi_2$...

When we obtain the velocity vector for position vector (r, θ, φ) Why do we take the time derivative of the radial part in the 3D Spherical Coordinate system only? Don't we need to consider the polar angle and azimuthal angle part like (dr/dt, dθ/dt, dφ/dt)?

Homework Statement Assume that a ball of charged particles has a uniformly distributed negative charge density except for a narrow radial tunnel through its center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton anywhere along the...

I'm trying to derive what ##ds^2## equals to in spherical coordinates. In Euclidean space, $$ds^2= dx^2+dy^2+dz^2$$ Where ##x=r \ cos\theta \ sin\phi## , ##y=r \ sin\theta \ sin\phi## , ##z=r \ cos\phi## (I'm using ##\phi## for the polar angle) For simplicity, let ##cos...

Homework Statement There is charge placed in a volume of a sphere, whose density changes by expression ρ(r)=ρ0a/r for 0<r≤a and ρ(0)=0. Where a and ρ0 are known variables , and r is a distance from the origin. Determine the potential of the point A(0,0,0) with regard to reference point at...

So I was asked to compute loop contributions to the Higgs and compute the integrals in spherical coordinates, I gave a look to Halzen book but did not found anything. Why, when and how to make that change?

Homework Statement Evaluate \int \int \int _R (x^2+y^2+z^2)dV where R is the cylinder 0\leq x^2+y^2\leq a^2, 0\leq z\leq h Homework Equations [/B] x = Rsin\phi cos\theta y = Rsin\phi sin\theta z = Rcos\phiThe Attempt at a Solution [/B] 2*\int_{0}^{\pi/2}d\phi \int_{0}^{2\pi}d\theta...

Hi! I have trouble with solving this problem and would be really thankful for some help. :) 1. Homework Statement Inside a thin, spherical metal-shell with a radius of 50 cm, a smaller homogenous metal-sphere with a radius of 20 cm is placed concentrically. The smal sphere is grounded through...

So it says here that a conducting sphere of radius R with a charge Q uniformly distributed over its surface has V = Q/4πεR , using infinity as the reference point having zero potential,,V (∞) = 0. This gives C = Q/|ΔV| = Q/(Q/4πεR)=4πεR. Does ,V (∞) mean that you are taking the potential of a...

In Dodelson's "Modern Cosmology" on p.241 he states that the ##a_{lm}##-s -- for a given ##l##-- corresponding to a spherical harmonic expansion of the photon-temperature fluctuations, are drawn from the same probability distribution regardless of the value of ##m##. Dodelson does not explain...

Homework Statement Homework EquationsThe Attempt at a Solution for ##r \le a## and ##l = 0##, the radial equation is $$- \frac {\hbar^{2}}{2m} \frac {d^{2}u}{dr^{2}} - V_{0} = Eu $$ $$- \frac {\hbar^{2}}{2m} \frac {d^{2}u}{dr^{2}} - [V_{0} + E]u = 0$$ call ##k^{2} = \frac...

When it comes to waves, spherical harmonics are, like, da bomb. I'm no expert - probably obvious from the question - but it seem to me that an instrument which maximises the utilisation of harmonics/resonances would be spherical. And yet, I can think of no spherical instruments - the most...

Hi, Set up the triple integral in spherical coordinates to find the volume bounded by $$z = \sqrt{4-x^2-y^2}$$, $$z=\sqrt{1-x^2-y^2}$$, where $$x \ge 0$$ and $$y \ge 0$$. $$\int_0^{2\pi} \int_0^2 \int_{-\sqrt{4-x^2-y^2}}^{\sqrt{4-x^2-y^2}} r\ dz\ dr\ d\theta$$

There are two spherical shells in different sizes and they are concentric. Now if I connect a battery to the two spheres (connect the negative pole to the smaller sphere and connect the positive pole to the bigger sphere). Will this system become stable? Or is there any situation for the charges...

How much electric flux linked with the spherical shell having a hole?(consider the charge is outside the shell) I knew the flux linked with spherical shell is zero.(because it is closed loop.)

Homework Statement The gradient, divergence and curl in spherical polar coordinates r, ∅, Ψ are nablaΨ = ∂Φ/∂r * er + ∂Φ/∂∅ * e∅ 1/r + ∂Φ/∂Ψ * eΨ * 1/(r*sin(∅)) nabla * a = 1/r * ∂/∂r(r2*ar) + 1/(r*sin(∅)*∂/∂∅[sin(∅)a∅] + 1/r*sin(∅) * ∂aΨ/∂Ψ nabla x a = |er r*e∅ r*sin(∅)*eΨ | |∂/∂r ∂/∂∅...

Homework Statement I have a field w=wφ(r,θ)eφ^ (e^ is supposed to be 'e hat', a unit vector) Find wφ(r,θ) given the curl is zero and find a potential for w. Homework Equations I can't type the matrix for curl in curvilinear, don't even know where to start! I've been given it in the form...

There are two spherical shells in different sizes and they are concentric. Now if I connect a battery to the two spheres (connect the negative pole to the smaller sphere and connect the positive pole to the bigger sphere). Will this system become stable? Is there any situation for the charges on...

The angular equation: ##\frac{d}{d\theta}(\sin\theta\,\frac{d\Theta}{d\theta})=-l(l+1)\sin\theta\,\Theta## Right now, ##l## can be any number. The solutions are Legendre polynomials in the variable ##\cos\theta##: ##\Theta(\theta)=P_l(\cos\theta)##, where ##l## is a non-negative integer...

1-capacitance of sphere with radius r : 4πεr 2-capacitance of 2 concentric spheres with inner radius a and outer radius b : 4πε(a.b/b-a) 3-when the outer the outer sphere is earthed it gives the same capacitance as in number 2 4-when the inner sphere is earthed it gives the sum of capacitances...

Homework Statement An ideal gas satisfying the Maxwell-Boltzmann distribution is leaking from a container of the volume V through a circular hole of area A'. The gas is kept in the container under pressure P and temperature T. The initial number density (concentration) is given by n0=N/V...

Homework Statement The question asks me to convert the following integral to spherical coordinates and to solve it Homework EquationsThe Attempt at a Solution just the notations θ = theta and ∅= phi dx dy dz = r2 sinθ dr dθ d∅ r2 sinθ being the jacobian and eventually solving gets me ∫ ∫ ∫...

I need to think of all the physics principles to explain how one can stack spherical items (ex. baseballs) on top of each other. So far I've thought of one. 1. Newton's third law In this case, the reaction is the normal force in each baseball that is stacked and the action is the force of...

Homework Statement ##x=r\sin\theta\cos\phi,\,\,\,\,\,y=r\sin\theta\sin\phi,\,\,\,\,\,z=r\cos\theta## ##\hat{x}=\sin\theta\cos\phi\,\hat{r}+\cos\theta\cos\phi\,\hat{\theta}-\sin\phi\,\hat{\phi}## ##\hat{y}=\sin\theta\sin\phi\,\hat{r}+\cos\theta\sin\phi\,\hat{\theta}+\cos\phi\,\hat{\phi}##...

Hi I am looking for an equation of intersection of 3 circles or 3 spheres, on the surface of the fourth (central) sphere, in a spherical coordinate circle. This should really be just a simple trilateration problem. I know this is usually done by transforming the spherical coordinate system to...

I'm at it again today. Helping the same friend (plus another) study for their final calculus exams; it's a good refresher for me as well. (I'm a senior industrial engineering major so I'm "done" with calculus, and it isn't used much in our upper level classes nor professionally to the best of...

Homework Statement A ball is rolling down from the top of a rough spherical dome with negligible initial velocity and angular velocity. Show that the ball must slide before losing the contact with the dome. Homework Equations ΣF=ma Στ = Fr = Iα fs = μsN vcm = rω Δmgh = 0.5mvcm2 + 0.5Icmω2 I =...

Homework Statement The space between two spherical shells kept at potentials V1 and V2, respectively, is filled with a dielectric medium. Find the electrostatic energy on the medium. Homework EquationsThe Attempt at a Solution I know how to get the energy if I am given the electric field or...

This thread is not about the lorentz invariance of the wave equation: \frac{1}{c^2}\frac{\partial^2\Phi}{\partial t^2}-\Delta \Phi = 0 It is about an interesting feature of a standing spherical wave: A\frac{\sin(kr)}{r}\cos(wt) It still solves the wave equation above, when it is boosted in...

Homework Statement A hollow spherical conductor, carrying a net charge +Q = 47 pC, has inner radius r1 = 5.9 cm and outer radius r2 = 11.9 cm. At the center of the sphere is a point charge +Q/2. a. Find the potential at r = 18.0 cm. b. Find the potential at r = 10.0 cm. c. Find the potential...

i am a beginner and was going through (Donald Mcquarie's "quantum chemistry" ) some discussion regarding orbitals of H-atom but i didn't get the logic behind writing px and py orbitals as linear combinations of spherical harmonics? according to what i understood, a given spherical harmonic in...

Homework Statement A vase is filled to the top with water of uniform density f = 1. The side profile of the barrel is given by the surface of revolution obtained by revolving the graph of g(z) = 2 + cos(z) over the z-axis, and bounded by 0 ≤ z ≤ π. Find the mass of the vase. Homework...

Homework Statement My textbook states that when ##\theta = c ## where c is the constant angle with respect to the x-axis, the graph is a "half-plane". However, when ##\phi = c ## it is a half-cone. The only difference I see is that ##\phi## is the angle with respect to the z-axis, rather than...

Homework Statement Plotting a point in spherical coordinates means using the format ##(\rho, \theta, \phi)## in place of ##(x, y, z)##. Taking a triple integral means replacing ##dV## with ##\rho ^2 sin(\phi) d\rho d\theta d\phi ## As you can see, ##\rho, \theta, \phi ## are all in the same...

I am studying the Earths main magnetic field (internal, specifically the stuff at the Core-Mantle boundary) which has led me to spherical harmonics. I am curious... how is the structure of a spherical harmonic determined by its degree l and order m? What role do the first three coefficients...

Hello, I am watching a video about spherical harmonics, and I am at the point where the color map is being shown for various values of ##l## and ##m## My question is, what am I supposed to make of these plots? Pretty colors yes, but what do these things mean?

Homework Statement You are blowing air into a balloon at a rate of 4*pi/3 cubic inches per second. (The reason for this strange-looking rate is that it will simplify your algebra a little bit.) Assume the radius of your balloon is zero at time zero. Let r(t), A(t) and V(t) denote the radius...

Homework Statement The potential difference Δϕ between the plates of a spherical capacitor is kept constant. Show that then the electric field at the surface of the inner sphere will be a minimum if a=(1/2)b, find that minimum. Where: a=radius of the inner sphere, b=radius of the outside...

Hey! :o Using spherical coordinates and the orthonormal system of vectors $\overrightarrow{e}_{\rho}, \overrightarrow{e}_{\theta}, \overrightarrow{e}_{\phi}$ describe each of the $\overrightarrow{e}_{\rho}$, $\overrightarrow{e}_{\theta}$ and $\overrightarrow{e}_{\phi}$ as a function of...

Homework Statement The plates of a spherical capacitor have radii 51.8 mm and 55.0 mm. (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance? (givens) a = 51.8 mm b = 55.0 mm d = 3.2 mm ε0 = 8.85E-12...

Homework Statement [/B] There are two spherical conducting shells one inside the other. If the total charge on the inside shell is -3q and the total charge on the outside shell is +5q what's is the charge on the inner and outer surface of each shell? Attempt at solution My teacher said i...

Homework Statement Attached. Homework Equations The Attempt at a Solution Hi, Ok, so for the first part of this question it asks to evaluate the integral of the dot product between A and dS. The magnitude of dS is as shown above, and it is in the radial direction in spherical polar...

Homework Statement What equation is needed to calculate the height of a spherical cap with a fixed volume and radius? Homework Equations V=πh/6 (3a^2 + h^2) Where V = volume, h is cap height, a is cap radius The Attempt at a Solution I have tried to separate the h out and got as far as...

Homework Statement R = 4000mi phi = 60 Me = 5.972E24 kg Mm = 5.972E16 kg distance of procession = 100 mi Homework Equations I know the answer is supposed to be ~1010 years. I also know what I am trying to do is have that e3 axis be pointing straight up, then when the mountain is placed on...

Hi I want to ask you if you know hot to write cos(theta)cos(phi) in terms of spherical harmonics? Thanks

After setting up Laplace's equation in spherical coordinates and separating the variables, it is not clear to me why the constants are put in the form of l(l+1) and why m runs from -l to l. Could anyone please help me ununderstand, or better yet, point me to a source that explains the entire...

Homework Statement So, probably a general question for most of all. It states that there is a charged insulating spherical shell with an inner radius of a/4 (a cavity) and an outer radius of a. The outer shell has a non-constant volume charge density of ρ=(-8α(r^2)). I need to find the electric...

Homework Statement a conducting spherical shell has radius R and potential V. If you want, you can consider it to be part of a capacitor with the other shell at infinity. you compress the shell down to zero size while always keeping it spherical,while a battery holds the potential constant at...