Sphere Definition and 1000 Threads

1. Homework Statement a point mass is projected at an angle of 60° from the horizontal. it collides with the sphere at a maximum height of trajectory with a sphere of radius of 72.5cm such that it is projected off the sphere once again at an angle of 60° from the horizontal.The sphere, due to...

Given sphereRadius and piVal, compute the volume of a sphere and assign to sphereVolume. Use (4.0 / 3.0) to perform floating-point division, instead of (4 / 3) which performs integer division. public class SphereVolumeCalculator { public static void main (String [] args) { double piVal...

Homework Statement In a lecture demonstration, a professor pulls apart two hemispherical steel shells (diameter D) with ease using their attached handles. She then places them together, pumps out the air to an absolute pressure of p, and hands them to a bodybuilder in the back row to pull...

Homework Statement Calculate the potential of a uniformly polarized sphere directly from eq. 9 Homework Equations V(r)=k \int \frac {P(r') \cdot \hat{r}} {r^2} d\tau The Attempt at a Solution P is a constant and can be factored out. Since r is taken, call the radius of the sphere R and and...

I've been wondering how I can find the pressure water exerts on a sphere it's in. As for cyllinders and pyramids, and prisms - the thing is extremely easy - you just take the one formula and put in numbers. What about a situation when we have a sphere whose radius is R, and it's half full with...

Homework Statement 1. The field for an infinite charged sheet is found to be σ/2ε0. If we place 2 infinite sheets of opposite charge above one another, we say that the field in between the sheets is σ/ε0 due to the superposition of individual fields. Why can't we say the same for a situation...

Homework Statement A uniform solid sphere of mass M and radius R is fixed at a distance h above a thin infinite sheet of mass density σ. Obtain the magnitude of the force between the sphere and the sheet. Homework EquationsThe Attempt at a Solution I've found the gravitational field from the...

Suppose that we have a hollow sphere (spherical shell) whose surface is held at some constant potential V0. What is the potential inside the sphere? I had an argument with my physics professor over this. He claims that the potential inside depends on how far you are from the center and becomes...

Homework Statement Homework Equations potential energy = -kQq/r potenial = kQ/rThe Attempt at a Solution i am not quite sure how does l play a part in this experiment since it is far away l is insignificant and the only initial energy is kinetic energy and final is kinetic and electric...

Homework Statement A small sphere with mass 5.00×10−7 kg and charge +6.00 μC is released from rest a distance of 0.400 m above a large horizontal insulating sheet of charge that has uniform surface charge density σ = +8.00 pC/m2.Using energy methods, calculate the speed of the sphere when it is...

Homework Statement My questions are just related to part a of this problem. Homework EquationsThe Attempt at a Solution I know that potential inside a conductor is equivalent to potential on the surface of the conductor and potential at any point is an algebraic sum of potential...

Hi PF! Attached is an figure from Bird Stuart and Lightfoot. I'm wondering if anyone can comment about the difference in spacing of these streamlines assuming each streamfunction is evenly spaced (or does this requirement make this picture invalid)? My interpretation assuming each...

Wikipedia(https://en.m.wikipedia.org/wiki/Photon_sphere): 'This equation entails that photon spheres can only exist in the space surrounding an extremely compact object (a black hole or possibly a neutron star)' But how can a neutron star? I have a doubt because 1. When а mass of а star...

Homework Statement A metallic sphere is charged. Where will the charges go? At center or on surface or uniformly distributed. Homework Equations I think it should be uniformly distributed. Cause that's why we have terms like volume charge density like we do q/volume. The Attempt at a Solution...

I had a question regarding calculating the area of a circular cap on a sphere. From what I’ve read, the area should be calculated according to; $$A = 2πr^2 \cdot (1 – cos (\frac{θ}{2} )$$ However, I have another way but I don’t understand why this isn’t correct. The circular area can be...

Homework Statement A thick, spherical shell of inner radius a and outer radius b carries a uniform volume charge density ρ. Find an expression for the electric field strength in the region a<r<b. Homework Equations Gauss's Law ∫E⋅dA Area of a sphere The Attempt at a Solution I know I am...

Homework Statement A uniform spherical ball of mass M and radius R, initially spinning about a horizontal axis with angular speed ω0, is placed gently on the floor. The initial center-of-mass velocity of the ball is zero. Derive that the moment of inertia ICM of the ball about an axis passing...

Homework Statement A sphere of radius r_s is at the center of a spherical shell of inner radius r_i=10\, r_s and thickness s = 10\, {\rm cm}\ll r_i. The sphere has a temperature T_s=1073\, {\rm K} and and an emissivity e=0.90. The inner surface of the shell has a temperature T_i = 873...

I know that in a sphere or other geometric conducting objects there is no E field inside because all the charge resides on the outside of the object canceling any inside field , although if I were to focus an electron gas in a vacuum chamber in some circular shape , all the electrons would want...

I am currently studying C Hammond's "Basics of Crystallography and Diffraction" (third ed.). In the first chapter ,concerning hard sphere model, I have found the following statement: There are, in fact, no examples of elements with this structure because, as the model building shows,the atoms...

Homework Statement A solid conducting sphere of radius R and carrying charge +q is embedded in an electrically neutral nonconducting spherical shell of inner radius R and outer radius 2 R . The material of which the shell is made has a dielectric constant of 3.0. Relative to a potential of...

Homework Statement A solid conducting sphere of radius R and carrying charge +q is embedded in an electrically neutral nonconducting spherical shell of inner radius R and outer radius 9 R . The material of which the shell is made has a dielectric constant of 2.0. Relative to a potential of zero...

****EDIT****: I had improper significant figures. It was the correct number. 1. Homework Statement The electric field on the surface of a 6.0 cm -diameter sphere is perpendicular to the surface of the sphere and has magnitude 52 kN/C . What is the magnitude of the electric flux through the...

Homework Statement this is a theoretical question.please consider the situation as follows: we are charging a metallic sphere using induction phenomenon with the help of a postively charged metallic rod and while on grounding the electrons flow from the ground to the sphere rather than sphere...

Homework Statement Homework EquationsThe Attempt at a Solution I figured you could consider it as infinitely many rings? Here is what I did so far: I feel like 0 is the wrong answer. Can anyone help me? Thanks.

I need to start by saying that I'm not a physicist, nor a student of physics. I'm a translator, and my text is about rotations around the azimuthal nodal lines on the sphere. I need to find a name for a particular type of a rotation operator, which rotates the sphere around the x and y axes...

Homework Statement Two identical 9.60-g metal spheres (small enough to be treated as particles) are hung from separate 500-mm strings attached to the same nail in a ceiling. Surplus electrons are added to each sphere, and then the spheres are brought into contact with each other and released...

question 1 The vector field F(x, y, z) = 2xi + 2yey2+z j +(ey2+z + cos z) k is conservative. Find a corresponding potential function. * e raise to power (Y square +z) Question 2 Consider a solid sphere of radius R, a cylindrical shell of outer radius R, inner radius a, and height h, and a...

Hello everyone. I've been doing a bit of independent study for this topic without much background and so my thermodynamic knowledge is fairly limited. I came across this problem and I'd like some assistance with it! If anyone can help out, I would be very grateful. A lot of the equations came...

Ok so we all know that when rolling down a fixed incline under gravity, a sphere will beat a cylinder in a race due to the fact that it has less rotational inertia. However, in the following set up, the cylinder beats the sphere. Say the cylinder and sphere are side by side on a horizontal...

I'm confused with the electric field inside a sphere. The book said that E=keQr/a^3 While one of the properities of electrostatic equilibrium mentioned that the E-field is zero everywhere inside the conductor. Are there any exceptional cases? Thanks in advance.

Homework Statement Find the potential of an uncharged metal sphere provided that a point charge q is located at a distance r from its center 2. The attempt at a solution As far as the charges are concerned , some negative charges will build up at the side of the charge because of induction ...

Homework Statement Find the magnetic dipole moment of a spinning sphere of voltage ##V## and radius ##R## with angular frequency ##\omega##. Homework EquationsThe Attempt at a Solution To find the dipole moment, we need to do ##I \int d \vec{a}##, which would be ##I 4 \pi R^2 \hat{r}##, but I...

$\tiny{s6.12.13}$$\textsf{Find an equation of the sphere}\\$ $\textsf{that passes through the point (4,3,-1) and has center (3,8,1)} $ \begin{align}\displaystyle(x-3)^2+(y-8)^2+(z-1)^2&= r^2\\\sqrt{(3-4)^2+(8-3)^2+(1+1)^2}&=r^2\\\sqrt{1+25+4}&=\sqrt{30}^2=30 =r\end{align}$\textit{so far ??}$

Firstly I appologize, that I am not native english speaker and I don't study physics(but cybernetics we are getting just some general knowledge about physics), but hopeffuly I will write this right. Homework Statement We know that inside of a conductive object is protected from influence of...

$\tiny{s6.12.11}\\$ \begin{align} &\textsf{(a) Find an equation of the sphere with center (1, -4, 3) and radius 5. }\\ &(x - 1)^2 +( y +4)^2 +(z - 3 )^2 = 5 ^2=25 \\ \\ &\textsf{(b) What is the intersection of this sphere with the xz-plane?.}\\ &\textit{assume it is an equation of a circle...

Homework Statement A non-conducting sphere of radius a carries a non-uniform charge density. The electrostatic field inside the sphere is a distance b from is center and is given by E = (b/a)4E0 (E0 being the maximum magnitude of the field.) a. Find an expression for E0 in terms of the...

Homework Statement Let me just put this here: http://i.imgur.com/dgcWAC3.png . Homework Equations E_flux=EA=(q_encl)/(permittivity) Area=4pir^2 The Attempt at a Solution Whenever I manipulate the above equations, I get a term of the form R/r, which implies, R being 5 cm, and r being the...

Homework Statement A solid sphere rolls down a hemisphere from rest. Find the angle at which the sphere loses contact with the surface. R = radius of hemisphere a = radius of sphere Homework Equations ΣFr = Macm,r N-mgcosθ = -mVcm2/(R+a) N = mgcosθ - mvcm2/(R+a) eq. (1) Conservation in...

Is the potential across the boundary continuous for a dielectric sphere embedded in a dielectric material, so that the potential inside the sphere can be set equal to the potential outside of it at r=R ?

The volume form on the unit sphere ##S^{n}## in ##\mathbb{R}^{n+1}## is given by $$i_{{\bf r}}\ dx^{1}\wedge \dots \wedge dx^{n+1}=\sum (-1)^{i-1}x^{i}dx^{1}\wedge\dots \widehat{dx^{i}} \dots \wedge dx^{n+1}.$$ Why must the volume form ##dx^{1}\wedge \dots \wedge dx^{n+1}## act on the vector...

This is a fiction project, but the question is about 3D geometry (a bit beyond my HS math skills). Given two points on a sphere (oh say, hypothetically, the Earth), draw a line from point A through the Earth to Point B. If I were to stand on point A and point directly at point B, what...

Schwarzschild coordinates for the Schwarzschild black hole solution become very weird near the event horizon because the radial coordinate is based on the proper circumference of a sphere but that has a minimum at the event horizon. This is easy to see in isotropic coordinates, where the...

Homework Statement Suppose W is the region inside the cylinder x^2+y^2=a^2 and inside the sphere x^2+y^2+z^2=b^2, where 0<a<b. Set up an iterated integral for the volume of W Homework Equations x^2+y^2+z^2=b^2 x^2+y^2=a^2 0<a<b The Attempt at a Solution I converted to cylindrical coordinates...

Homework Statement A solid sphere with radius ##R## is submerged on water at a depth ##h_1##. Water's specific weight is ##\gamma##. Determine both horizontal and vertical forces exerted by the water on the surface of the sphere, in terms of ##R## and ##\gamma##. Homework Equations My lecturer...

Homework Statement A metal sphere of radius ##a=1cm## is charged with ##Q_a=1nC##. Around a sphere is placed a spherical shell of inner radius ##b=2cm## and outer radius ##c=3cm##. The electrical potential of the shell in refenrence to a point in the infinity is ##V=150V##. The spheres are in...

Homework Statement A sphere of mass M and radius R is not necessarily solid or hollow. It has moment of inertia I = cMR^2 . The sphere starts from rest and rolls without slipping down a ramp from height H. It then moves back up the other side with height h, but now with no friction at all...

Say I have a solid sphere of mass on a horizontal surface. If suddenly there was a spherical hole(shape of a sphere) off center, will the sphere suddenly move? And there is no friction between the ground and the sphere. I'm assuming that it will. But my reasoning is this, the sphere suddenly...

i used to get pauli matrices by the following steps it uses the symmetry of a complex plane sphere i guess so..? however i can't get the 8 gell mann matrices please help ! method*: (x y) * (a b / c d ) = (x' y') use |x|^2 + |y|^2 = |x'|^2 + |y'|^2 and |x| = x * x(complex conjugate) this way...

Homework Statement A sphere of radius R contains two spherical cavities. Each cavity has a radius of R/2 and touches both the outside surface of the sphere and its center as shown. The mass of a similar sphere without the cavities is M. Find the force of attraction on a small particle of mass m...