Sphere Definition and 1000 Threads

A solid sphere has surface charge density, Rho (r) Rho(r) = k 1 ( 0 < r < a) k2 x ( a < r < R) 2) Find the electric field in all region i.e 1) r < a and 2) a < r < R and 3 ) R < The attempted solution and the question with the diagram is attached below Could the answer be verified...

Homework Statement (Problem 2.38 From Griffth's Electrodynamics): A metal sphere of radius R, carrying charge q, is surrounded by a thick concentric metal shell (inner radius a, outer radius b). The shell carries no net charge. Find the surface charge density ##\sigma## at R, a, and b...

I've been trying to wrap my head around equidistant points, like platonic solid vertices inside a sphere where the points touch the sphere surface. This led me to the strange and unusual world of mathematical degeneracy, henagons, dihedrons, and so on, along with the lingering question of...

Homework Statement A sphere of radius R carries charge Q. The distribution of the charge inside the sphere, however, is not homogeneous, but decreasing with the distance r from the center, so that ρ(r) = k/r. 1. Find k for given R and Q. 2. Using Gauss’s Law (differential or integral form)...

Homework Statement I have a sphere, it's imperfectly spherical, I put it on an incline and apparently it needs a minimum friction to start rolling or moving. Homework Equations I = 2/5 MR^2 torque = I*alpha = R x F The Attempt at a Solution [/B] before anything, I don't get why there's a...

Homework Statement A hollow conducting sphere has inner radius R and outer radius 1.5R. A +40nC point charge is placed at the center. What is the total charge on the interior and exterior walls of the sphere? R=10cm Homework Equations Gauss's Law σ = Qenc/A The Attempt at a Solution I'm not...

Does a sphere made of an elastically anisotropic material (eg. a material of cubic symmetry) subject to an hydrostatic pressure retains its spherical shape ?

Homework Statement A solid sphere with radius R=12 m has charge Q=3 nC distributed uniformly throughout its volume. (a) Calculate the potential difference between a location at infinity and a location on the sphere’s surface. (b) Calculate the potential difference between a location on the...

Homework Statement Two otherwise identical, small conducting spheres have charges +6.0 µC and −2.0 µC. When placed a distance r apart, each experiences an attractive force of 9.1 N. The spheres are then touched together and moved back to a distance r apart. Find the magnitude of the new force...

I'm designing a valve that uses a ball to seal the valve. When the valve is empty there is no force acting on top of the ball. When water flows in, it will push up on the ball to dislodge it, water will flow into the valve and push the ball up until it seats into the top hole/chamfer which then...

Homework Statement Consider a solid spinning sphere of negative charge in a non-uniform magnetic field: http://d2vlcm61l7u1fs.cloudfront.net/media%2F2f8%2F2f840122-3d7f-4af3-98a7-efa9b2e7d26a%2FphpBOhfaK.png (the rotation illustrated at the top is supposed to be counter-clockwise). What...

Homework Statement Consider a hollow cylinder of mass M with an outer radius R_out = 10 cm and an unknown inner radius R_in. If the hollow cylinder is to roll down an incline in the same time as a spherical shell of the same mass and the same outer radius, calculate R_in. Homework Equations...

Hi! So it's been a while since I've done this and uh I also haven't slept well over the past few days so literally nothing is clicking. I have so many questions about this celestial sphere business. Please bear with me. It also doesn't help that our notes have like 5 different diagrams of the...

Mod note: Moved from a technical forum section, so missing the homework template. @fab13 -- please post homework problems in the appropriate section under Homework & Coursework. I have the following exercise to solve : I have to find all the points on the surface ##x^2+y^2+z^2=36## (so a sphere...

Greg Bernhardt submitted a new PF Insights post The Schwarzschild Metric: Part 2, The Photon Sphere Continue reading the Original PF Insights Post.

Hi colleagues, I need your help to figure out some subtle theory problmes I have about this topic. I was thinking about a system composed by a conductive sphere (not grounded) under the effect of a pont charge placed near the sphere. As I know we need two image charges to satisfy the boundary...

Homework Statement In a spherical bowl a small ball is jumping around. The ball hits the bowl in two spots and moves in two different trajectories in times T1, T2. Find the radius of the bowl. Homework Equations Newton's laws of dynamics. The Attempt at a Solution The only thing I could...

Homework Statement Homework EquationsThe Attempt at a Solution Potential at the center of conducting charged sphere surrounded by a grounded shell If I take another sphere of charge –q of radius a with uniform charge density, then the potential on the spherical region from the radius a to...

Well, my physics teacher taught us about rotation the other day and I came across a scenario where a sphere and a ring roll down a friction-less inclined plane from a point of absolute rest. I found it counter-intuitive as I started to think about why would they start rolling in the first place...

Homework Statement Homework EquationsThe Attempt at a Solution Option (a), because the potential is 0 on the surface, and potential due to point charge is positive so there must be negative charge on the surface. Since opposite charges attract each other, there is an attractive force...

This is a well-known problem I think: take four arbitrary points on a sphere as the vertices of a tetrahedron. What is the probability that the centre of the sphere will be located within the tetrahedron? A friend gave me this puzzle to solve, and I came up with the answer P = 1/8. This is the...

Homework Statement A charged, straight line/rod of infinite length has a Discrete uniform distribution of charge, has a linear density of λ and is at a distance d from a sphere with a radius of R. Find the entirety of the Electrical Flux that is caused by this charged rod, which passes...

Homework Statement An uncharged, unconductive, hollow sphere with a radius R of 10.0 cm, surrounds an electric charge of 10.0 μC, which is found at the beginning of the axises, in a standard cartesian system. Parallel to the z axis, a small drill with a radius r = 1.00 mm opens a hole in the...

I need to draw electric field lines of sphere in uniform electric field with LaTeX/TikZ. Can anyone show me equation of field lines in polar coordinates?

Homework Statement What is the escape speed of an electron launched from the surface of a 1.0-cm-diameter glass sphere that has been charged to 10nC? Homework Equations Given: d= 1.0cm r= 0.05cm= 0.0005m q1 = 10nC = 10 x 10-9 (sphere) q2 = -1.6 x 10-19 (electron) Equation: U = (kq1q2)/r KE=...

Homework Statement Consider a conducting sphere of radius ##R_1##. Inside it there is a cavity, spherical in shape, with it origin at the same point as the conducting sphere and of radius ##R_2## ##(R_1>R_2)##. Assume there is a point charge equal to ##+Q## at the origin. Use Gauss law to...

Homework Statement When completely hollow. To what fraction of volume should water be poured into it so that it is just enough to cause the sphere to sink. [/B]Homework Equations Archemedes : Buoyant fource equals weight of water displaced The Attempt at a Solution Let's first find the...

Homework Statement A solid sphere of mass m=2.5 kg is rolling at v=5.3 m/s. Calculate the transitional kinetic energy, rotational kinetic energy, and the ratio of the two (Rotational/ Transitional). Homework Equations [/B] Inertia of solid sphere = 2/5 mR^2 (where R is the radius and m is the...

Homework Statement I am trying to show that the pressure drag acting on a sphere is 2πμaU by integrating around the surface of the sphere where U is the speed of the fluid the sphere is in, a is its radius, and μ is the viscosity. Homework Equations The pressure at a given position r can be...

Homework Statement A gas effuses into a vacuum though a small hole of area A. Show that if the particles effused into an evacuated sphere and the particles condensed where they collided that there would be a uniform coating. (7.6 of Blundell and Blundell) Homework Equations Angular...

Homework Statement Using the method of images discuss the problem of a point charge q inside a hollow grounded conducting sphere of inner radius a.Find (a) the potential inside the sphere (b) induced surface-charge density (c) the magnitude and the direction of force acting on q is there any...

So, I'm really bothered with something. Let's suppose there's a simple pendulum with a rigid sphere on it's end. In order to get the motion equations I thought we could use two approaches. One would be using rigid body dynamics (torque, moment of inertia ...), the other one would be using...

Homework Statement A sphere of mass m2 and radius R rolls down a perfectly rough wedge of mass m1. The wedge sits on a frictionless surface so as the sphere rolls down, the wedge moves in opposite direction. Obtain the Lagrangian. Homework EquationsThe Attempt at a Solution Here's my diagram...

Homework Statement A spherical shell of radius R has a surface charge distribution σ = k sinφ. Calculate the dipole moment of the spherical shell. Homework Equations P[/B]' = ∫r' σ(r') da' The Attempt at a Solution So I believe my dipole will be directed along the y axis, as the function...

Homework Statement Find the z -coordinate of the center of mass of the first octant of a sphere of radius R centered at the origin. Assume that the sphere has a uniform density. Homework Equations Mass = Integral of the density function Center of mass for z = Integral of density * z divided...

Since the universe's expansion is accelerating, let's suppose it will expands at a higher rate of 700 km per s per megaparsec (10 times the present value) in future. Then the Hubble radius would be 430 megaparsecs (0.1 times the present value). So shouldn't the Hubble sphere contract instead...

This space is homotopy equivalent to the complement of the three coordinate axes in ##R^3##. This is in the chapter about the Seifert-Van Kampen Theorem, so I'm expecting to invoke that theorem. The thing is, how should we choose our open sets such that the intersection is path connected and...

Homework Statement Show that any geodesic with constant ##\theta## lies on the equator of a sphere, with the north pole being on the ##\theta = 0## line. Hence explain why all geodesics on a sphere will be arcs of a great circle. Homework EquationsThe Attempt at a Solution I've had a go at it...

So if I have a sphere of uniform charge distribution, the electric field at one point away from the circle would be affected by ALL individual charges distributed across the circle, right? From the picture I drew, there would only be a net effect of E-field in the X direction because there...

The Euler Characterist of the projective plane and sphere is given by V - E + F. V is vertices, E is edges, F is faces. A presentation of the projective plane is {a | aa} and a presentation of the sphere is {b | bb^1} Yet the Euler characteristic is 2 for the sphere and 2-n for the connected...

Homework Statement A uniform charge density of 700 nC/m3 is distributed throughout a spherical volume of radius 6.00 cm. Consider a cubical Gaussian surface with its center at the center of the sphere. [reference picture] What is the electric flux through this cubical surface if its edge...

$\tiny{15.4.17}$ Find the volume of the given solid region bounded below by the cone $z=\sqrt{x^2+y^2}$ and bounded above by the sphere $x^2+y^2+z^2=128$ using triple integrals $\displaystyle\int_{a}^{b}\int_{c}^{d} \int_{e}^{f} \,dx\,dy \,dz$ not real sure where to to start with this?

Homework Statement A mass point is sliding down from the top of a hemisphere, with an initial speed of zero. I want to determine the angle ##\theta## at which the mass point will lift off the surface of the hemisphere. Homework EquationsThe Attempt at a Solution We can determine the speed...

Hi All, Consider an elastic sphere which is homogeneously charged and suferring an harmonic inflation and deflation. Is it correct to explain the theoretical result that it does not emmit radiation, even though all of its charge elements are accelerating, as a systematic effect of destructive...

Homework Statement The rectangular parallelepiped with sides ## a > b > c ## is filled with charge of constant density ## \rho ##. A sphere of radius ## 2a ## is constructed with its center at the origin. Find the flux through the surface of this sphere Homework Equations $$ \oint E \cdot...

While looking at stereo ahead images some shots look like there is a massive sphere that appears and disappears in the camera example of this can be found here : http://www.dailymail.co.uk/news/article-3953058/NASA-cameras-capture-huge-blue-spherical-object.html as you can see the sphere appears...

Is Sphere a more generalized form of Cone i.e. formed by 2 dimensional rotation to 360° of a cone? Or is Cone a more generalized form of Sphere since sphere can be formed by rotating about Z axis a zero eccentric planar intersection of a cone? @fresh_42 @FactChecker @WWGD

Homework Statement Consider a glass sphere completely filled with water except for a small air bubble at 1 atmosphere. The sphere is accelerating to the right. What is the pressure at the center of the sphere? Let Pe = Atmospheric pressure r = radius of sphere pw = density of water a =...

Homework Statement A sphere with a charge of -3.5 x 10^-9 C and a radius of 1.0x10^-2 m is located at the origin of a coordinate system. What is the electric field 1.75 x 10^-2 m away from the center of the sphere along the positive y axis? Homework Equations e = kQ/r^2 The Attempt at a...

Homework Statement A uniformly magnetized and conducting sphere of radius R and total magnetic moment m = 4\pi MR^3/3 rotates about its magnetization axis with angular speed \omega. In the steady state no current flows in the conductor. The motion is nonrelativistic; the sphere has no excess...