Sphere Definition and 1000 Threads

Homework Statement Given two vector fields ##W_ρ## and ##U^ρ## on the sphere (with ρ = θ, φ), calculate ##D_v W_ρ## and ##D_v U^ρ##. As a small check, show that ##(D_v W_ρ)U^ρ + W_ρ(D_v U^ρ) = ∂_v(W_ρU^ρ)## Homework Equations ##D_vW_ρ = ∂_vW_ρ - \Gamma_{vρ}^σ W_σ## ##D_vU^ρ = ∂_vU^ρ +...

Homework Statement Given a sphere with radius R, centered at (0,0,0), it's dipole density given as ##P\left(\vec{r}\right)=\alpha\left(R-r\right)\hat{z}## where r is the distance from the center of the ball. I'm required to find: Bound charge density inside the sphere, bound charge density on...

1. Homework Statement Homework EquationsThe Attempt at a Solution I did this : 1/2 (2.7x10^-6)(150x10^3) - 1/2 (1.575x 10^-6)(75x10^3) =0.143 J But the answer is 0.15 , where did I did wrong?

I am given the sphere V= x^2 + y^2 + z^2 =< 1 I have converted it to spherical coordinates: x = rsin(t)cos(f) y = rsin(t)cos(f) z = rcos(t) where t ranges from 0 to pi, and f ranges from 0 to 2pi. I am unsure how to go about this problem from here. Any guidance would be really appreciated :)

Please excuse the obscurity of the question but say there are two spheres: sphere A has a radius of 1 metre and sphere B has a radius of 2 metres. Both sphere have super- luminous velocites (they are both exactly c/H metres from us) and due to the extent of their velocities they will begin to...

Say there is a theoretical sphere of radius r, at rest, then if it's velocity changes then I assume that the radius is subject to length contraction and thus it's volume would decrease from a stationary observer. Is this assumption true?

Hi, I recently tried to derive the equations for a geodesic path on a sphere of radius 1 (which are supposed to come out to be a great circle) using the formula \dfrac{d^2 x^a}{dt^2}+\Gamma^a_{bc} \dfrac{dx^b}{dt}\dfrac{dx^c}{dt}=0 for the geodesic equation, with the metric...

Homework Statement A metal sphere is subjected to a heat flux, 5000 W/m2. It is originally at 20 C. How long does it take to heat to 90 C? D = 5 cm density = 8522 kg/m3 cp = 0.385 kJ/kg-K k = 104 W/m-k Homework Equations rate of heat input = rate of heat accumulation -k*A*dT/dr = m*cp*dT/dt...

1. Homework Statement Why is there no electric field strength in a metal sphere? Is it because the sum of the individial electric field strength of the charges in the sphere is zero? How is that possible? Homework EquationsThe Attempt at a Solution

Homework Statement A marble rolls from the top of a big sphere. What is the angle θ when the marble is about to leave the sphere? Assume a zero speed at the top. Homework Equations The question came from the chapter Mechanics - circular motion. The Attempt at a Solution I can't conceive what...

Homework Statement A sphere has a diameter of ##D = 2\rho = 4cm##. A cylindrical hole with a diameter of ##d = 2R = 2 cm## is bored through the center of the sphere. Calculate the volume of the remaining solid. (Spherical or cylindrical coordinates?) hint: Place the shape into a convenient...

Hello.. i just saw this amazing Forum and wanted to contribute, so here is my first question and i hope i get an answer x.d I was told that at electrostatic equilibrium, the electric field inside a conducting sphere will be ZERO, How can i charge thissphere from the inside, so the Electric...

Homework Statement The density of the charge inside of the sphere is given- ro=a*r+b/r The electric potential on the outer layer of the sphere is phi=0 The radius of the sphere is 58.4m r-is the distance from the center of the sphere What is the electric potential when r=15.4m? Homework...

Hi Community, I have this tutorial question. When I look at the first question (a) I think it is FALSE as the surface area would not increase at the same rate as the radius. For the second question I am not sure if I am interpreting it correctly. If $$r=\sqrt{\frac{Ct}{4\varPi}+2}$$ where...

Homework Statement Homework Equations ΔPE = G × M₁ × M₂ (1/Ri - 1/Rf) where G = gravitational constant M₁ = mass of one object M₂ = mass of the other object Ri = initial distance Rf = final distance ΔPE = -ΔKE The Attempt at a Solution My solution is v = 2√(GM/d). I am making sure it is...

Hello, This question is from 1990 Turkey National Physics Olympics. I tried my best to translate it clearly. 1. Homework Statement https://s23.postimg.org/cotn29afv/Hollow+Spherical+Glass.jpg The sphere of radius 2R has an empty sphere inside with radius R. In order for the image of an object...

I'm studing Gauss law for gravitational field flux for a mass that has spherical symmetry. Maybe it is an obvious question but what are exactly the propreties of a spherical simmetric body? Firstly does this imply that the body in question must be a sphere? Secondly is it correct to...

Hi If I'm using this method to generate points inside a sphere with radius K: X = S^(1/3)*sqrt(1-V^2)*sin(O) Y = S^(1/3)*V Z = -S^(1/3)*sqrt(1-V^2)*cos(O) where (0 < s < K^3), (-1 < v < 1) and (0 < o < 2*pi), i guess that: S_PDF(s) = 1/(K^3) V_PDF(v) = 1/2 O_PDF(o) = 1/(2*pi) How come the...

Homework Statement A sphere (of radius r and mass m) rotating with angular velocity ω0 is lowered onto the edge of a floating platform of length L and mass M. The platform can move freely on water. The platform is rough and the sphere rolls all the way from one edge to the other edge of the...

Homework Statement An uncharged metal sphere hangs from a nylon thread. When a positively charged, nonconducting glass rod is brought close to the metal sphere, the sphere is drawn toward the rod. But if the sphere touches the rod, the sphere suddenly flies away from the rod. Explain why the...

Homework Statement Find the mass M of a sphere of radius a, if its mass density is proportional to the distance from the center of the sphere. Homework Equations Triple integrals using spherical coordinates The Attempt at a Solution The only place where I am stuck is if the density is KpcosΦ...

Homework Statement "How much energy is released when a sphere of constant density (p) with mass (M) and radius (R) is put together gravitationally? What you should do is to think of the energy released when a shell is brought in from infinite distance (where potential energy of zero) to the...

Homework Statement A metal sphere of charge +6μC is surrounded by a metal shell of net charge +6μC. Which of the following diagrams represents the electric field lines of the system? Homework EquationsThe Attempt at a Solution The correct answer provided by my teacher is a figure with 12...

Could you perform Static structural analysis on this solid sphere? No contacts to be used. I do not have any specific boundary conditions(unable to apply constraints to a complete solid spherical body) All i know is the pressure that needs to be applied. You could consider a smiley ball on...

Homework Statement Homework Equations How to locate the point P and C after 0.5s from their initial position ? The Attempt at a Solution Well i don't know whether it would be correct way to start the problem i.e find the centripetal acceleration .

Homework Statement Hi everybody! Still checking my comprehension of physics, and hopefully those posts will help other users! A homogeneous wooden sphere with mass M and radius R rotates about a perpendicular axis going through its center of mass. At the top of this axis is a homogeneous...

Homework Statement Homework Equations What is gauge pressure ? The Attempt at a Solution How to find gauge pressure ?

In the example my textbook has, the electric potential is calculating by integrating the electric field from infinity to R, radius of sphere, and then integrating the electric field from R to r, radius of point inside sphere. What I don't understand is why is the field integrated from infinity...

Hey, (I have already asked the question at http://physics.stackexchange.com/questions/244586/bloch-sphere-interpretation-of-rotations, I am not sure this forum's etiquette allows that!) I am trying to understand the following statement. "Suppose a single qubit has a state represented by the...

1. Homework Statement I need to find the total charge inside the small metal sphere, inside the big metal sphere as well as outside the big metal sphere. Homework Equations What confuses me is the electric field vector. Since it's only poiting in one direction it can't originate from a...

I found a funny model of the qubit written by Aerts in Foundations of quantum physics: a general realistic and operational realistic and operational approach. At the beginning the qubit is at the point P on the Bloch sphere. It will be measured along another direction (two opposite points on...

Homework Statement Consider two metal spheres, sphere 1 having radius R1 = 20 cm, and sphere 2 having a radius R2 = 10 cm. The two are rather close to one another, separated by a center-to-center distance of only 80 cm. Suppose now that they are connected to each other by a thin wire that is...

Hello All I could get some help I would greatly appreciate it. I am trying to figure how to calculate the dissolution time of sphere undergoing constant corrosion at a rate of corrosion. Through a little google-fu, I found an article which gives me the solution (...

Hello! (Wave) A sphere with radius $10 cm$ and center $(0,0,0)$ turns around the $z$-axis with angular velocity $4$ and with such a direction that the rotation has counterclockwise direction, being seen my the positive semi-axis $z$. I want to find the rotation-vector $\omega$. Is this equal...

I have a free particle moving on the surface of a sphere of fixed radius R. Gravity is ignored and m/2 is left out since its constant. The lagrangian is L = R^2 \dot{\theta^2} + R^2 sin^2{\theta} \dot{\phi^2} Using the Euler Lagrange equations I obtain sin^2{\theta} \dot{\phi} = A = const \...

Hi Guys, I'm reading Roger Penrose's book "The Road to Reality" at the moment and I wonder if you could help me out with a pretty simple derivation which he doesn't describe in complete detail. On page 399 he considers a sphere of mass contracting under gravity, and says "The rate of volume...

Metal ball ( Figure 5) radius a = 5 cm , is surrounded by two concentric metal shell of radius b = 10 cm and c = 15 cm , and d = 20 cm and e = 25 cm . The relative permeability of the dielectric between the ball and the first shell , and between the two shells is εr is 4. Outside the outer cross...

Homework Statement A torus has a major radius and a minor radius. When R>r by a magnitude of at least 4x, it comes to be a slim ring looking shape. When R>r by a magnitude of 1/2, the shape looks to be a donut. When R=r, the torus shape looks more like a sphere except with a small gap in the...

Homework Statement Hello everyone, I am new here and have a question regarding method of images in my electricity and magnetism class. I need help to even get the ball rolling. The question is as follows: a) What is the image of a dipole, oriented toward the center of the conducting sphere, if...

Dear All, I want to calculate water pump required for lifting the 1.5m dia. Granite ball on 3mm water sheet. kindly help ma as the earliest. Thanks Snadeep

Hi, I have an interesting problem. I have three GPS coordinates, creating two lines across the surface of a sphere (assuming the Earth is spherical). I want to be able to create a new line (across the surface of a sphere) with a gradient that is in between the gradient of the two existing...

Homework Statement Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. At what distance from the center of the sphere does the...

Homework Statement A sphere with mass 0.4 kg circles around a circular trajectory with ray 2 m and angular speed 12 rad/S. Which is the momentum of the impulse of the sphere? Homework Equations L=Iw=2/5mr^2w w(angular speed) or L=mr^2w The Attempt at a Solution I think we should use the first...

Homework Statement [/B]Homework Equations Poynting's Theorem S = 1/μ0 (E x B) Momentum = p = μ0ε0 ∫ S dτ The Attempt at a Solution My strategy was to treat the hollow sphere as a point charge (by Gauss' Law), so E = 1/4πε0 Q/a2. I believe the magnetic field would be B = 2/3μ0M (where M is the...

As many of you know, using the stereographic projection one can construct a homeomorphism between the the complex plane ℂ1 and the unit sphere S2∈ℝ3. But the stereographic projection can be extended to the n-sphere/n-dimensional Euclidean space ∀n≥1. Now what I am talking about is the the...

Homework Statement A sphere of radius R = 1.40 m surrounds a particle with charge Q = 42.0 μC located at its center as shown in the figure below. Find the electric flux through a circular cap of half-angle θ = 28.0°. Homework Equations Φ = ∫E⋅dA E = (kq)/r2 A = πa2 where a = rsin(θ) --> from...

There's this question, A conducting sphere of radius R and charge Q is placed near a uniformly charged non conducting infinitely large thin plate having surface charge density σ. The potential at point A on sphere due to charge on sphere is? I have uploaded the picture. Now I know the net field...

hi guys, i have a question. i saw this picture, and i don't really understand how they derived with the formula. The aim is basically to find the formula for the surface area of a spherical cap. why do you differentiate the x=sqrt(rˆ2-yˆ2)? how does that help to find the surface? and then...

I'm totally confused what the question is asking. I do not know how to start... please help A charged sphere with 1×108 units of negative charge is brought near a neutral metal rod. The half of the rod closer to the sphere has a surplus charge of 2×10^4 units. What is the magnitude of the...

I've been given a copy of my friend's midterm exam from this same class from last term, and decided to take a crack at it to help study. One question type in particular really messes me up and it looks like the following. How would I go about solving these in the future? A solid insulating...