Shell Definition and 784 Threads

I have been going over previous tests in an attempt to better prepare myself for the final that is coming tomorrow. I was posed a question. Use the shell method to find the volume of the solid generated by revolving the plane region about the given line. y = 4x - x^2 , y = 0, about the line x...

Homework Statement Consider two concentric spherical metal shells of radii 2m and 4m, situated in free space and carrying uniform surface charge densities of 20nC/m2 and 5nC/m2 respectively. Find the capacitance C=Q/ΔV of the spherical capacitor formed by the shells. Here Q is the total...

can someone please provide me with a proof or even just an intuitive explanation

Homework Statement Consider a thick metal shell with inner radius a = 2cm and b = 4cm. The shell carries no net charge. A point charge of q = 3nC is placed at the centre of the shell. Find the total charged induced on the inner boundary of the shell. Find the total charge induced on the outer...

ITS NOT A HOMEWORK PROBLEM PROBLEM::- THINK OF A CYLINDRICAL SHELL WITH NUMEROUS SPHERICAL HOLES ALL AROUND IT. (FOR EG. http://sell.lulusoso.com/upload/20120317/Underground_Water_Pipe.jpg) HOW TO FIND VOLUME & SURFACE AREA OF SUCH A CYLINDRICAL SHELL. (A GENERALIZED CASE FOR N HOLES AROUND...

Shalom We are used to hearing that Coulomb's law doesn't settle with the relativity principle that nothing moves faster than the speed of light, in the sense that it embeds 'Action in a Distance'. Meaning that if somthing changes in r1 at time t1, and we write the law for any t before...

Homework Statement The region in the first quadrant bounded by the lines y=4 and x=2 and the curve x^2=4y is revolved about the y-axis. Find the volume: a) by the method of washers b) by the method of shells Homework Equations The Attempt at a Solution I drew the region, and I...

I'm in undergrad doing research with a professor. He's leaving for vacation for a few weeks, and has tasked me with a project. I've been analyzing some spectra for some Carbon reactions, and he posed a question to me on why we don't see other higher-energy states, even if the experiment is ran...

Homework Statement Find the volume of the solid generated by revolving the region bounded by the curve y= e^(x^2) and the lines y=0, x=0, and x=1, about the y-axis. Homework Equations Shell method?The Attempt at a Solution I don't know which method to pick, disk/washer or shell method? I picked...

Hello MHB, Consider the region bounded by the lines x=0,y=1 and curve y=\sin(x), 0\leq x \leq \frac{\pi}{2} decide the volume when it rotate in y-axe ( Tips: t=\sin^{-1}(y) can be usefull) I got pretty confused what my integral limit shall be. I know the formula will be \pi\int_a^b xf(x)^2 ...

I am trying to understand the implications of the Birkhoff theorem as it applies to a cavity within a spherically symmetric, stationary thin shell. Is the region of space-time within the cavity described by the actual Minkowski metric diag{1,-1,-1,-1}, or is it some other metric with constant...

Homework Statement Volume of solid rotated about x-axis x=1+y^2, y=1, y=0, x=0 using shell method Homework Equations The Attempt at a Solution so i set up the integral with ∫2pi(y)(1+y^2)dy from 1 to 2 which is apparently wrong, but i don't know why.

Homework Statement A conducting cylindrical shell has it's axle on Ox axis, inner radius R1 and outer radius R2. If the volume current density is given by the formula \vec{j}(r)=J0\frac{r}{R1}\hat{i} where J0 is a constant and r the distance from the cylinder's axle, calculate the magnetic...

I am having few doubts while studying electric field which i am putting here Suppose there is a spherical metallic shell with point charge q1 at the center and q2 charge outside the sphere in space ... 1) Now what I have have read in this forum and on other places is that the induced charges...

I must be thinking way to hard about this problem. Can someone please give me a nudge in the right direction? Homework Statement A shell traveling with speed v0 exactly horizontally and due north explodes into two equal mass fragments. It is observed that just after the explosion one...

What I understand is this: Shell theorem states that the force of gravity is focused at the center of an object. But, say that there is a large planet with a gravitational force equal to that of earth's. It is perfectly round… and hollow. Since it is hollow, how large would it be to have Earth's...

how do you prove that the maximum no. of electrons in the nth shell of an atom is twice of n squared (2n^2)

We can easily find from gauss's theorem(or otherwise) the field inside and outside a uniformly charged spherical shell.But i was wondering what would be the field on the surface of the shell.

1. Homework Statement [/b] A solid cylindrical conducting shell of inner radius a = 4.9 cm and outer radius b = 6.1 cm has its axis aligned with the z-axis as shown. It carries a uniformly distributed current I2 = 7.4 A in the positive z-direction. An inifinte conducting wire is located along...

Homework Statement A current of constant density, J0, flows through a very long cylindrical conducting shell with inner radius a and outer radius b. What is the magnetic field in the regions r < a, a < r < b, and r > b? (Use any variable or symbol stated above along with the following as...

Homework Statement A hollow spherical shell carries charge density \rho=\frac{k}{r^2} in the region a<=r<=b, where a is the inner radius and b is the outer radius. Find the electric field in the region a<r<b. I'm not allowed to use integral form of Gauss's law, must use differential...

Homework Statement A solid conducting sphere with radius of R1 and charge of 3Q, is placed in the center of a thin conducting spherical shell with inner radius of R2 and outer radius of R3, charged with -Q what is the field for r<R1, R2>r>R1, R3>r>R2, r>R3 and what is the charge...

Homework Statement A copper resistor has the shape of a cylindrical shell. What is the resistance of this resistor if its length is 1m, its inner radius is 0.1cm, and its outer radius is 0.2 cm? What is the radius of a solid wire of circular cross section with the same length and the same...

Hello there! I have a question regarding the behavior of test particles inside a slowly rotating thin spherical shell of matter under the influence of the gravito - magnetic "lorentz force" (this is all in the weak field slow motion approximation). I want to see just how analogous I can claim...

Solving "poisson's equation" slowly rotating spherical shell of mass Homework Statement We have that \partial ^{\alpha}\partial _{\alpha}\bar{\gamma _{0\mu}} = -16\pi T_{0\mu} which is very similar to Poisson's equation if we treat each component of the metric tensor as a scalar field (the...

How many grams of copper are required to make a hollow spherical shell having an inner radius of 5.70 cm and an outer radius of 5.75 cm? The density of copper is 8.92 g/cm^3. Ok, so, how do I find the height? Or solve the problem without the height?

Homework Statement use the shell method to find the volume of the solid given by y = 4x - x2 y = x2, about the line x = 4 The Attempt at a Solution I have to find a height and a radius multiply them together and integrate them over some bounded region, fair enough. My functions intersect...

Homework Statement Given the following curve: y = x^3 Use shell method and rotate around x-axis to determine the volume bounded region: y = 8, x = 0 Homework Equations 2pixyThe Attempt at a Solution x(x^3) = x^4 Integrate x^4 = 1/5 x^5 1/5(8)^5 = 6553.6 *2 = 13107.2 pi the answer should be...

Homework Statement Homework Equations The Attempt at a Solution I'm not sure if I am doing part a,b,e, and f correctly

Homework Statement Using the shell method, set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = x3 bounded by y = 8, and x = 0. Homework Equations volume of a solid revolved around x-axis using the shell method.The...

Homework Statement use the shell method to find the volume of the region rotated about the x-axis.Homework Equations y=3x+10 y=x^2The Attempt at a Solution 2∏ (integral) (0 to 25) [ (y) (sqrt(y) - (y-10)/3) dy ]

"closed electron configuration" equivalent to "closed shell" Hi, is the term "closed electron configuration" equivalent to "closed shell"? derivator

Homework Statement use the shell method to find the volumes of the solids generated by revolving the region about the indicated axis. Homework Equations x=18(y^2 - y^3) about line y=8/5. The Attempt at a Solution 2∏∫ (0 to 1) (8/5 - y) (18y^2 - 18y^3)

Homework Statement Find the volume of the solid generated by revolving the region bounded by y=4x-x^2 and y=x about the y-axis and about the line x=3. Homework Equations 1. y=4x-x^2 and y=x 2. y=4x-x^2 and x=3 The Attempt at a Solution 1. 2∏∫ (0 to 3) (x)(4x-x^2 -x) dx 2. 2∏∫...

Homework Statement Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and the lines about the x-axis.Homework Equations Y=|x|/3 , Y=1The Attempt at a Solution 1. 2∏∫(0 to 2) (y) (Y/4 - (-Y/4)) dy 2. y^3/6] (0 to 2) Answer: 8∏/3 (which...

I have noticed an issue I must resolve before writing a GUI for my FORTRAN program in Linux. If I move into the directory (cmd line) and type ./myprogram it works fine. It reads the input file from that directory and creates an output file. If I run it from the file manager it gives me 2...

Homework Statement Determine how many integrals are required for disk, washer, and shell method.Homework Equations x=3y^2 - 2 and x=y^2 from (-2,0) to (1,1) about x-axis.The Attempt at a Solution Since there are no breaks or abnormalities in the graph it appears that 1 integral will solve for...

Homework Statement A thin ,metallic spherical shell contains a charge Q on it. A point charge q is placed at the center of the shell and another charge q1 is placed outside it as shown in the figure .All the three charges are positive. Q.1 The force on the charge at the center is a) towards...

In this physics textbook, in the part where it is introducing atoms and in particular, electron shells. it says: "the first and inner most shell has a capacity for 2 electrons, the outermost shell has a capacity for 32 electrons" I thought the outermost shell always had a maximum capacity...

"As the ball gets deeper under the surface of the Earth, the layers above it stop exerting gravitational force, and all that matters is the mass underneath." How to justify this sentence is true?

Hey everyone, I'm currently running a program which accepts an input file. The input file has various parameters, 3 of which I need to change, run again, etc. The range of those 3 parameters are 15 values for one, 12 values for another and 10 for another, so I have 15*12*10 (=1800) possible...

I've always learned that putting energy-photons into an atom can bump an electron up to a "higher energy state", and that when the electron "falls" back down into a lower energy state, it then emits a photon, and so forth. What I never seem to find, however, in these descriptions are any...

"After a shell explodes at the top of its trajectory, the center of gravity of the fragments has an acceleration, in the absence of air resistance, equal to g and downward." Why isn't there an x-component? I get why there would be a downward component with a = g, but shouldn't there at...

Hello guys, I am calculating Bending and Shear stresses in hollow beams. We have a particular kind of shell that we use for impact loading, so we put rubber discs around the steel shell. So my question is, how will it affect the moment of inertia ? Since I know that the rubber discs will...

Homework Statement A +30 mC point charge sits at the center of a spherical thick metallic shell, of 4.0 cm inner radius and 2.0 cm thickness. The net charge of the shell is -50mC. a.) Determine the location of the 0 volt equipotential surface. b.) calculate the electric potential of the...

Homework Statement A +30mC point charge sits at the center of a spherical thick metal shell, of 4.0cm inner radius, and 2.0cm thickness. The net charge on the shell is -50mC. Homework Equations The Attempt at a Solution I came up with several conclusions and I'm not really sure...

Homework Statement Use the shell method to find the volume of the area enclosed by: y= 16-x^2 , y= 16,x=4, around y=16 Homework Equations 2\pi\int (shell height)( shell radius) The Attempt at a Solution I tried using the disk method and obtained \frac{1024}{5}*\pi but I'm...

Just a quick question concerning the concept mentioned in the title to make some clarification. Does an object have to be located at the center of the hollowed out space in a spherical shell (with uniformly distributed mass) for the net gravitational force to be zero? In other words, at the...

Homework Statement Determine the electrostatic energy, W, of a spherical shell of radius R with total charge q, uniformly distributed. Compute it with the following methods: a) Calculate the potential V in spherical shell and calculate the energy with the equation: W = (1/2) * ∫σVda...

Homework Statement A solid metal cylinder of radius R and length L, carrying a charge Q, is surrounded by a thick coaxial metal shell of inner radius a and outer radius b. The shell carries no net charge. Find the potential at the center, using r=b as the reference point. Homework...