Sphere Definition and 1000 Threads

Hi! Here is my task: Calculate area of cylinder $$x^{2}+y^{x}=ax$$ sliced by sphere $$x^{2}+y^{2}+z^{2}=a^{2}$$. Here is graph: How to do it? If problem was "Calculate area of sphere $$x^{2}+y^{2}+z^{2}=a^{2}$$ sliced by cylinder $$x^{2}+y^{x}=ax$$" I would solve it using double integrals...

Homework Statement So I was given the equation that in a sphere, if at a distance r outisde a sphere of radius R (The sphere insulated, I guess it matters since it would prevent charge to leave?) The electric field E = kqR/r^3 I'm not sure how they got this Homework Equations Flux = Integral...

Homework Statement find the values of the integral \int_{S} \vec A\cdot\ d\vec a where, \vec A\ = (x^2+y^2+z^2)(x\hat e_{1}+y\hat e_{2}+z\hat e_{3}) and the surface S is defined by the sphere R^2=x^2+y^2+z^2 Homework Equations first i must evaluate the integral directly, so i don't...

Homework Statement One of two nonconducting spherical shells of radius a carries a charge Q uniformly distributed over its surface, the other a charge -Q, also uniformly distributed. The spheres are brought together until they touch. What does the electric field look like, both outside and...

Homework Statement Homework Equations The sphere is positively charged and appears to have its charge concentrated at its centre. Potential V is calculate to be 285V The Attempt at a Solution The charge induced on inside of box is negative. THe potential is less. It is said that it's being...

Homework Statement Sphere of a radius R=50 cm is in nonmagnetic medium of permittivity ε=4. EM wave with amplitude of electric field Em= 200 V/m is spreading through the medium. How much energy pass through surface of sphere through 1 minute? I have couple of question here. Since the sphere...

This is strictly a geometric question from Lemaitre's writing. He is presenting an example of a closed space represented as a sphere (I'm assuming the surface only?), and makes a "displacement" of the sphere to demonstrate a point. I am not following his operation on the sphere based on any of...

Hello, I have to compare the real solution of the electric field radiated by a sphere, having 10 cm radius, charged with 1e-012 C (perfect conductor), something like E=f(x) where x is distance from the sphere, from 0m (surface of the sphere) to 1m, with numerical solution. I tried Ansoft...

Homework Statement Imagine an iron sphere of radius ##R## that carries a charge ##Q## and a uniform magnetization ##\vec{M} = M\hat{z}##. The sphere is initially at rest. (a) Compute the Angular momentum stored in the electromagnetic fields. (b) Suppose we discharge the sphere, by connecting a...

I know that the Casimir Effect Force is calculated by the equation F=(π h c A) / 480 L4. However, how can you calculated the Casimir Force if there is for example, a bubble. If there is a sphere how can you calculate the force because I don't know what the area would be or how to find it.

Homework Statement Assume I want to calculate the electric flux through a spherical surface centred at point P with radius R which contains a point charge Q, that is not concentric with the spherical surface. Here, I can no longer assume that ∫∫sEdA = E.A, and I have to calculate the value of...

Hey people, first post, I'm sorry if I'm posting this in the wrong place. How do you calculate the force exerted on a sphere? I'm building a pneumatic air rifle, and I'm trying to figure out how fast an airsoft bb accellerates with a certain pressure. The projectile is 6mm in diameter, so...

why do heavier balls fall faster in liquids ?, if F=mg-drag, a heavier ball would have greater mg, but the acceleration is given by F=ma, therefore mg-drag = ma, a = (mg-drag)/m. I can't see how a heavier ball would fall faster.

Homework Statement [/B] A uniform solid ball of mass m rolls without slipping down a right angled wedge of mass M and angle θ from the horizontal, which itself can slide without friction on a horizontal floor. Find the acceleration of the ball relative to the wedge. 2. The attempt at a...

Homework Statement So I'm calculating the gravitational potential of a sphere at at point P. R = radius of sphere, r = distance from center of sphere to point P. I'm looking at two scenarios; r > R (1) and r < R (2). So I have the following integral: \begin{equation} V(r) = \int...

Some 2D creatures are living on a sphere that it radius in increasing over time. They think that they are living on a expanding plane. The max speed of information is speed of light. The life time of the creatures are very smaller that the radius divided by speed of light. How can they find out...

1. The problem statement, all variables and given/known Sphere A has a mass=4.2X10^-2 kg and iA tethered to a wall by a thin thread. Excess of electrons for A=1.2X10^12 Excess of electrons for B=3.5X10^12 Distance between A and B=0.23m find the angle between the thread and the wall Homework...

Im having trouble convincing myself that a charge located anywhere inside a conducting sphere will create an induced charge on the surface of the sphere with an electric field that is completely uniform. This doesn't make much sense to me. Also same with how the electric field inside solid...

Consider a pendulum in it's balance point hanging from ceiling. It can swing in all the directions in the space. The pendulum can only swing in a sphere(the string can't bend). Now, is it possible to release the pendulum in a particular height and with a initial condition that in the first...

A body moves through a fluid, a retarding force due to turbulence may be experienced. In case of a sphere of radius R moving with speed v through a stationary fluid of density p which it at rest, this force is given by F = kp (R^2) (v^2) k is a constant. Why F is proportional to kp (R^2) (v^2) ?

The problem is as follows: There is a point magnetic dipole embedded at the center of a sphere (radius R) of linear magnetic material of permeability μ. What is the magnetic field inside the sphere? I know that this problem has been solved in many books.But I am trying a different method. Since...

Hi all. This is my first question on these forums. I am given a task to test out whether or not FD=1/2 CDAρv2 is a good model to test drag force. Where CD is described by Reynold's Number. We have a balloon a small ball and a myriad of basic physics lab equipment.What is a experiment I could...

Homework Statement A 25.0 g copper ring at 0°C has an inner diameter of D = 2.71585 cm. A hollow aluminum sphere at 88.0°C has a diameter of d = 2.72019 cm. The sphere is placed on top of the ring (see the figure), and the two are allowed to come to thermal equilibrium, with no heat lost to the...

Homework Statement http://web.phys.ntnu.no/~ingves/Teaching/TFY4240/Exam/Exam_tfy4240_Dec_2013.pdf http://web.phys.ntnu.no/~ingves/Teaching/TFY4240/Exam/Solution_tfy4240_Dec_2013.pdf problem 2g Homework EquationsThe Attempt at a Solution Hi, this is taken from problem 2g in the problem set...

< Moderator Note -- Thread moved from the technical PF Calculus forum >[/color] I can't seem to grasp the idea of this problem, any help is much needed. The problem reads, "As a spherical raindrop falls, it reaches a layer of dry air and begins to evaporate at a rate that is proportional to...

Consider this: We have a sphere rolling down a slant, released from some height h with null velocity. At the end of the slant its potential energy will have been fully converted to kinetic energy, part translational and part rotational. Now consider this: at the end of the slant the ball enters...

Homework Statement a sphere of uniform density and radius R is floating on water , partially immersed such that the distance between the top of the sphere and the water surface is R/2 find the density of the sphere Homework Equations Archimedes Principle The Attempt at a Solution One can...

Homework Statement This is example 3.9 in Griffiths Electrodynamics. "A specified charge density σ(θ) (inclination angle) is glued over the surface of a spherical shell of radius R. Find the resulting potential inside and outside the sphere." The problem suggests that although it is possible to...

Homework Statement [/B] A sphere 100 mm diameter is to be coated with chromium from a solution containing chromium in the six valent (hexavalent) state. How much time would be needed to produce a coating 20 μm thick if: • the current is 20 A • the cathodic efficiency is 15% • the atomic weight...

prove that the quotient space obtained by identifying the points on the southern hemisphere, is homeomorphic to the whole sphere.I am trying to define a homeomorphism between the quotient space and the sphere,and i need help doing it. Thank's in advance.

Homework Statement A hot solid sphere of initial radius ##a## with a uniform initial temperature ##T_{0}## is allowed to cool under stagnant air at ambient temperature, ##T_{\infty}## . Assume the temperature within the sphere is uniform throughout the cooling process. Show that under...

Homework Statement A spherical nonconductor of radius a carries charge +Q uniformly spread through its volume. 2 hemispherical conducting shells of inner radius b and outer radius c are placed concentrically with the nonconducting sphere to form a single conducting sphere. The conducting shell...

Is it true that the atlas for a torus can consist of a single map while the atlas for a sphere requires at least two maps? Can we ever get by with a single map for some Calabi–Yau manifolds assuming that question makes sense? If not is there some maximum number required? Thanks for any help!

Homework Statement Hello, I have to calculate the self-energy of an uniform charged electron with radius R. The distributed charge is e. Homework Equations The SE is given as: E=\frac{1}{2}\int dV \int dV' \frac {\rho(\vec r)\rho(\vec r')}{ |\vec r - \vec r'|} according to the problem sheet...

The problem goes by this: A sphere of radius ##\rho## is constrained to roll without slipping on the lower half of the inner surface of a hollow cylinder of inside radius R. Determine the Lagrangian function, the equation of constraint, and Lagrange's equations of motion. Find the frequency of...

Homework Statement A dielectric sphere radius R is injected with free charge so that the resultant polarization can be described by ## \vec P = \frac{K}{r} \hat r_1## where ##\hat r_1## is the unit radial vector. a) Calculate the volume and the surface density of bound charge b) Calculate the...

Homework Statement A solid spherical ball is placed carefully on the edge of a table in the position shown in the figure. The coefficient of static friction between the ball and the edge of the table is 0.5 . It is then given a very slight push. It begins to fall off the table. Find the angle...

Homework Statement A uniform solid sphere, of radius 0.20 m, rolls without slipping 6.0 m down a ramp that is inclined at 28° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest? Homework Equations KE=1/2Iw^2 PE=mgh I don't know what...

why does the Hubble sphere increase amd why is the Hubble constant called a constant if the value keeps changing.

Homework Statement Taylor, Classical Mechanics Problem 10.11 ** a) Use the result of problem 10.4 (derivation of the general integral for a moment of inertia of a continuous mass distribution in spherical coordinates, using point particles) to find the moment of inertia of a uniform solid...

Homework Statement Find the area of that part of the cylinder x^2 + y^2 = 2ay that lies inside the sphere x^2 + y^2 + z^2 = 4a^2. Homework Equations [/B] If a surface S can be parametrized in terms of two variables u and v, then dS = Norm[dR(u,v)/du x dR(u,v)/dv]. The surface area is given...

Homework Statement Find the energy required to assemble two uniform hollow spheres of charge q between radii a and b with a volume charge density roh-v. The shells are separated by a distance c. *description of picture* - two identical spherical shells with inner radius a and outer radius b...

Homework Statement Consider a nonconducting sphere of radius r2. It has a concentric spherical cavity of r1. The material between r1 and r2 has a charge density p (C/m3). Take V=0 and r=infinity. Determine the electrical potential V as a function of the distance r from the center for (a) r>r2...

Homework Statement Radioactive wastes are stored in a spherical stainless tank of inner diameter 1 m and 1 cm wall thickness. Heat is generated uniformly in the wastes at a rate of 30,000 W/m3. The outer surface of the tank is cooled by air at 300 K with a heat transfer coefficient of 100 W/m2...

Homework Statement A sphere with radius R = 0.200 m has density ρ that decreases with distance r from the center of the sphere according to \rho = 3.00 \times 10^3 \frac{kg}{m^3} - (9.00 \times 10^3 \frac{kg}{m^4})r a) Calculate the total mass of the sphere. b) Calculate the moment of inertia...

The problem statement Based on an analytical solution for the concentration profile of a dissolving sphere, I am supposed to use a numerical method to find the time at which the sphere has fully dissolved. This is not so much a question about specific values - but about the technique by which I...

I'm stuck on this problem: A small sphere is attached to a fixed point by a string of length =30cm , and whirls round in a vertical circle under the action of gravity at such speed that the tension in the string when the sphere is at its lowest point is three times the tension when the sphere is...

Homework Statement Suppose a grounded spherical conducting shell of radius R surrounds a pointlike dipole at the center with \vec{p}=p\vec{k} Find the potential V(r,\theta) for r <= R. Hint: Use spherical harmonics regular at r=0 to satisfy the boundary condition. Homework Equations General...

I've tried this problem at least 10 times using the equations in my book and I keep getting the same answer. What am I doing wrong? Homework Statement A solid steel sphere of density 7.6 g/cm3 and mass 0.2 kg spin on an axis through its center with a period of 1.5 s. Given Vsphere =4/3π^3, what...

Homework Statement A spherical conductor of radius ##a## carries a charge q and also there is a jelly of constant charge ##rho## per unit volume extending from radius ##a## out to radius ##b##. I'm looking to see if I got the correct set up for the electric field of this spherical conductor for...