Sphere Definition and 1000 Threads

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...

Use an appropriate volume integral to find an expression for the volume enclosed between a sphere of radius 1 centered on the origin and a circular cone of half-angle alpha with its vertex at the origin. Show that in the limits where alpha = 0 and alpha = pi that your expression gives the...

I realize that this is probably really basic, but I can't quite conceptualize a hollow metal sphere having constant voltage and zero electric field inside of it. I've searched around on the Internet, and I've seen stuff about Gauss' Law, but even after reading into that a little bit I can't make...

Inside a charged sphere, the electric field strength is zero because there are electrostatic forces from all directions. I can't understand why electric potential inside the charged sphere is maximum ?

Homework Statement Suppose light of momentum -P\hat{\textbf{k}} is shone on a sphere of radius R. What is the momentum transferred onto the sphere? Homework Equations The Attempt at a Solution I think the transferred momentum upon reflection is given by (-2P\hat{\textbf{k}} \cdot...

Homework Statement What is the diameter of a copper sphere that has the same mass as a 9.00 cm× 9.00 cm× 9.00 cm cube of aluminum? Density of Aluminum = P(al) = 2.70g/cm3 Density of Copper = P(cu) = 8.96 g/cm3 Volume of Aluminum Cube = Vcube = 729 cm3 Homework Equations Volume of a Sphere =...

I am trying to understand N-spherical cap area formula (surface area of blue part), but it seems to give wrong answers. for 1 dimensional cap obviously ## \frac{l_{cap}}{l_{sphere}}=\frac{l_{arc}}{l_{circle}}=\frac{r*θ}{r*2π}=\frac{θ}{2π} ## But according to wikipedia formula...

I would like to know the maximum voltage that a metal sphere can hold from applying negative charge to it. My thoughts are that the maximum voltage is the breakdown voltage of the surrounding medium (air in this case). I assume that at that voltage, electrons would arc from the sphere to the...

A sphere with radius "r" has three points on its surface, the points are A, B, and C and are labelled (xa, ya, za) and so on. What is the general formula to calculate the area on the surface of the sphere defined by these points?

Homework Statement See image attached. Oh it's part c by the way. Homework Equations maybe upthrust=weight of water displaced... None really relevant. The Attempt at a Solution I thought the balance would initially go up as the sphere entered the water, (but maybe slightly less than the...

Homework Statement A thin spherical shell of radius ## R ## rotates with angular velocity ## \Omega ##. Its total mass ## M ## is uniformly distributed. Find metric inside and outside the shell, assuming its small departure from the flat space-time. Find the angular velocity ## \omega ##...

So I derived the E-field of a hollow sphere with a surface charge σ at z and I got: E(r)=\hat{z}\frac{\sigma R^2}{2\varepsilon _{0}z^2}\left ( \frac{R+z}{\left | R+z \right |}-\frac{R-z}{\left | R-z \right |} \right ) at z>R, the equation becomes: E(r)=\hat{z}\frac{\sigma R^2}{\varepsilon...

Homework Statement http://physics.columbia.edu/files/physics/content/Quals2010Sec2.pdf Problem 1 Consider a rigid, ideally conducting sphere of radius R, with total charge zero. The sphere rotates with angular velocity Ω, ΩR<<c. Suppose a dipole magnetic field threads the sphere. the dipole is...

I have two metal half-spheres, each with a hole in the center. If I put these two together, perhaps with electrical tape, and apply a charge, how will the voltage due to the nonuniform charge distribution be different from that of a perfect sphere? I am assuming that the charge distribution...

so I got my sphere, centered at (1,-2,0) with radius 3 how do I put normal vectors/arrows onto my sphere's surface? I tried quiver3(x,y,z)

Hi, I wanted to see if I could understand Archimedes' proof for the area of a sphere directly from one of his texts. Almost right away I was confused by the language. Archimedes lists a bunch of propositions that eventually lead up to the 25th proposition where the area of the sphere is finally...

Homework Statement I need to know why my derivation does not work. I am attempting to derive I=2/5 mR^2Homework Equations I have seen people derive it using disks but my question is why do the shells not work? Where in my set up did I go wrong? Thanks The Attempt at a Solution I am attempting...

Homework Statement How do I find the surface area of a sphere (r=15) with integrals. Homework Equations Surface area for cylinder and sphere A=4*pi*r2. The Attempt at a Solution I draw the graph for y=f(x)=√(152-x2). A circle for for positive y values which I rotate. I will create infinite...

Homework Statement A sphere of radius .06 m and mass .5 kg rolls down a ramp that is angled 30 degrees down the incline. It starts rolling from a height of 7 feet and does not slip What is its final linear velocity? Now, I used mgh=translational +rotational KE and found that the final velocity...

Hello there ! I am writing here, because I could not find any good explanation in the literature and on the web Going straightaway to the point, my question is connected to Ewald's sphere and so called the limiting sphere. I red that limiting sphere is such a construction that appoints the...

Homework Statement A sphere of radius 10.0 cm floats in equilibrium partially submerged in water with its lowest point 5.00 cm below the water's surface. (a) What is the buoyant force acting on the sphere? Homework Equations F = pvg The Attempt at a Solution F= 1000 * v * 9.8 V=...

Homework Statement A conducting sphere of radius 100cm is charged to a potential of 30 volts. a) What is the charge on the sphere? b) What is the energy stored in the field? c) If the sphere is connected to a second identical uncharged sphere by a long wire, what is the final energy in the...

Homework Statement Evaluate the electric field of a hollow sphere with a dipolo , in a dialectric. See left figure.. Homework Equations $$\alpha \vec{p}$$ The Attempt at a Solution I don't understad why at the field electric "in" there is a term of form $$\alpha \vec{p}$$ , and term $$\beta$$...

Homework Statement Mountaineers are simulating a massive avalanche snowball by using a big Styrofoam ball (m = 75 kg; r = 1.50 m).They give it an initial impulse of 1500 kg m/sto start it rolling down the hill without slipping (no snow sticks to the ball, and ignore air resistance). Near the...

What is the direction of field inside a charged non-conducting sphere? Using gauss law, I can find the magnitude of electric field inside the shell by assuming a spherical Gaussian surface. But how can I find its direction? Also, if electric field exists inside a charged sphere, wouldn't the...

Homework Statement "Find the electric field due to a solid conducting sphere of uniform charge distribution using Coulomb's law and brute force integration only. Use Gauss' Law to verify the result. Homework Equations Coulomb's law for element field dE[/B] The Attempt at a Solution I...

Homework Statement A solid sphere is rolling without slipping on rough ground with an angular velocity w and linear velocity v. It collides elastically with an another identical sphere at rest. Radius of each sphere is R and mass m. What is the linear velocity of the first sphere after it...

I'm wondering about how one would describe the dynamics of a rotating sphere. Consider this: a solid sphere of mass "m" and radius "r" is set to rotate about a tangent to its surface. If it is released from the horizontal position such that it swings like a pendulum, what would be the force...

Homework Statement Wikipedia tells me that I can obtain the surface area of a sphere by realizing that the volume of a sphere is equivalent to the infinite sum of the surface areas of hollow, nested spheres, sort of like little Russian dolls. That makes sense, and then differentiating both...

Homework Statement Consider two solid dielectric spheres of radius ##a## separated by a dis- tance ##R## (##R\gg a##). One of the spheres has a charge ##q## and the other is neutral. We scale up the linear dimensions of the system by a factor of two. How much charge should reside on the first...

Hey, guys! I had a brief electromag question. If capacitance is defined as the amount of charge that can be stored in a capacitor per unit of potential difference, then technically can capacitors made from insulators still have a capacitance? The problem I'm considering is calculating the...

Hello guys, new member here. I've got a calculus project due Tuesday that I could use some help on. I won't bore you with the all details of the project, but first let's imagine an olive in the shape of a perfect sphere (with a radius always bigger than 6mm) that goes through a set of blades...

Homework Statement Find the electrostatic force of interaction between two halves of a spherical conductor of radius R carrying a charge Q. This thread already exists- https://www.physicsforums.com/threads/electric-force-between-two-halves-of-a-sphere.317380/ but is closed. Homework Equations...

Homework Statement Find the potential at the centre and at P of a hollow uncharged conducting spherical shell if a charge q is placed at a distance of 2r from centre of shell. (r is the radius) Homework Equations All the charge induced on the sphere has to reside on the sphere's outer...

An uncharged metal sphere suspended by a silk thread is placed in a uniform external electric field E.(a)What is the magnitude of the electric field of points inside the sphere?(b)Is your answer changed if the sphere carries a charge? I would have asked this in homework forum but it does not...

So you can solve the Stokes equation for flow around a sphere to obtain the pressure in the fluid: p=p0-3nuacosθ/2r2 where n is the viscosity, u is the speed of the fluid (along the z axis) far away from the sphere, a is the radius of the sphere and r,θ are the usual spherical polar coordinates...

A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that...

http://www.phys.uri.edu/gerhard/PHY204/tsl93.pdf To find electrical potential at r<R I want to know why should we subtract ##V##=-##\int_∞^R\frac{kQ}{r^2}\,dr##-##\int_R^r(0)\,dr##=##\frac{kQ}{R}## I don't know why are we subtracting these two?

Obviously, they exist as mathematical concepts, and those concepts are real, but in physical reality, everything is made up of subatomic particles and, if the theory is ever verified, strings. So if you try to construct a curve, circle or sphere, you are necessarily stacking a bunch of subatomic...

Homework Statement Suppose a charge is distributed in a lower half region of a sphere and the upper half has zero charge. What is the potential inside? Homework Equations Poisson Equation? The Attempt at a Solution My problem here is I don't know how to start, I think laplace equation can't...

Homework Statement how to divide moment of inertia of solid sphere about its central axis?. Solid sphere has radius R, mass M. Homework Equations I=∫r2dm 2/5 MR^2 The Attempt at a Solution https://photos.google.com/search/_tra_/photo/AF1QipPoXyad0q1Y3yisc0LeeJHGApkIrGbitK6kAk5p i try to...

Homework Statement Using the fact that \nabla \cdot r^3 \vec{r} = 6 r^2 (where \vec{F(\vec{r})} = r^3 \vec{r}) where S is the surface of a sphere of radius R centred at the origin. Homework Equations \int \int \int_V \nabla \cdot \vec{F} dV =\int \int_S \vec{F} \cdot d \vec{S} That is meant...

A solid sphere and a hollow one of same mass and radii are rolled down a rough inclined plane. Which of the following is true? (A) solid sphere reaches bottom with greater speed. (B) solid sphere reaches the bottom with greater kinetic energy. ( I know that option A is correct.Thus I felt that...

Homework Statement Hi, I'm currently answering a problem in Jackson's electrodynamics. The question is: Given a point charge q inside a hollow. grounded, conducting sphere of inner radius a. Find the potential inside. This can be solved by placing an image charge outside the sphere, and...

So the popular internet news outlets are ringing with articles about a possible Dyson sphere, or alien mega-structure around a star (KIC 8462852) 1500 light years away. Here is one such article : http://www.space.com/30855-alien-life-search-kepler-megastructure.html I'd like to know, since i...

Homework Statement Homework EquationsThe Attempt at a Solution so plugging in the variables, the density should be 0.002 with density known, and the volume of the sphere with radius 10, we can find the mass. (density x volume = mass) mass is about 16.75 kg it states the amount of charge...

Hello, So I am working on a project that requires the movement of iron nanoparticles (let's assume 25nm in diameter, and let's assume the sphere is uniform and pure iron) through a (non-magnetic) gel using an externally applied magnetic field. Let's assume the total distance I want to move the...

Homework Statement A sphere of radius R carries an electric charge Q, uniformly distributed inside its volume. (a) Using the expression for the electric field given in the lectures, compute the electrostatic potential V (r) inside and outside the sphere. Homework Equations E[/B] = -∇V The...

Homework Statement Consider a unit sphere centered at the origin. In terms of the Cartesian unit vectors i, j and k, find the unit normal vector on the surface Homework Equations A dot B = AB cos(theta) A cross B = AB (normal vector) sin(theta) Unit sphere radius = 1 The Attempt at a...