Spherical shell Definition and 203 Threads

Homework Statement Find the moment of inertia of a spherical shell (hollow) with mass M and radius R. Homework Equations ## I = \int r^2 dm ## The Attempt at a Solution This is method I use to find Moment of Inertia of solid sphere: We use circular cross sections. At some radius r...

I want to ask Is conducting shell same as uniformly charged thin spherical shell? Because while finding Electric field due to uniformly charged thin spherical shell surface charge density is taken the same happens in case of conducting/metallic shell all the charges reside on surface similarly...

Homework Statement Given a spherical shell of radius R and the surface charge density ( being the angle from the top of the sphere and being a constant) find the electric potential and the electric field inside and outside the sphere. Check that both the potential is continuous inside and...

Homework Statement A charged spherical insulating shell has inner radius a and outer radius b. The charge density on the shell is ρ. What is the magnitude of the E-field at a distance r away from the center of the shell where r < a? Homework Equations Gauss' Law The Attempt at a Solution I...

consider two concentric spheres, where inner radius is r and outer radius is r+delta. Assume space between the two spheres is mass of an amount to be solved for. Given the metric inside the sphere, assumed to be varying as implied by the Cosmic Background Radiation anisotropy (CBRa), can the...

Hi! I have trouble with solving this problem and would be really thankful for some help. :) 1. Homework Statement Inside a thin, spherical metal-shell with a radius of 50 cm, a smaller homogenous metal-sphere with a radius of 20 cm is placed concentrically. The smal sphere is grounded through...

How much electric flux linked with the spherical shell having a hole?(consider the charge is outside the shell) I knew the flux linked with spherical shell is zero.(because it is closed loop.)

Homework Statement A hollow spherical conductor, carrying a net charge +Q = 47 pC, has inner radius r1 = 5.9 cm and outer radius r2 = 11.9 cm. At the center of the sphere is a point charge +Q/2. a. Find the potential at r = 18.0 cm. b. Find the potential at r = 10.0 cm. c. Find the potential...

Homework Statement So, probably a general question for most of all. It states that there is a charged insulating spherical shell with an inner radius of a/4 (a cavity) and an outer radius of a. The outer shell has a non-constant volume charge density of ρ=(-8α(r^2)). I need to find the electric...

Homework Statement [/B] A thin spherical shell of radius R = 0.50 m and mass 15 kg rotates about the z-axis through its center and parallel to its axis. When the angular velocity is 5.0 rad/s, its angular momentum (in kg ⋅ m2/s) is approximately: a . 15 b. 9.0 c. 12 d. 19 e. 25 Homework...

Homework Statement A spherical shell of mass M and radius R is completely filled with a frictionless fluid, also of mass M. It is released from rest, and then it rolls without slipping down an incline that makes an angle θ with the horizontal. What will be the acceleration of the shell down the...

I am working on a design of a spherical dome. I tried to understand membrane theory with no success.Can anyone please help me with an clear explanation to derivation of membrane theory of shells.

Homework Statement A thin spherical shell of radius R carries a surface charge density of the form kcos 3 θ . Find the electric field inside and outside the sphere and demonstrate explicitly that its components satisfy the relevant boundary conditions at the surface Homework Equations The...

Homework Statement A thin spherical shell of radius R carries a surface charge density of the form kcos3 \theta Find the electric field inside and outside the sphere and demonstrate explicitly that its components satisfy the relevant boundary conditions at the surface. Homework Equations...

If there was a spherical shell with negative charge density and a positive point charge inside the shell, the electric field lines from the point charge would just be radially outward towards the shell right? What about the case where there's a positive charge density and a positive point...

Homework Statement A thick spherical shell with inner radius R and outer radius S has a uniform charge density d.(A) What is the total charge on the shell? Express your answer in terms of R, S, d, and π. (B) Express the electric field as a function of distance from the center of the sphere r...

Hey guys, I have a problem that is giving me trouble. Homework Statement I have to solve time dependent diffusion equation ##D\nabla^2 T(r,t)=\frac{\partial T}{\partial t}## (##D## is diffusion constant and ##T(r,t)## is temperature function) for a spherical shell of radii ##r_1## and ##r_2##...

As we know there are charge on spherical shell then electrical field inside the shell will be zero. 1) If there is no charge on the spherical shell, but has charge inside the shell then what is the electric field inside and outside the shell? 2) If there is charge on the spherical shell...

Homework Statement A conducting sphere of radius R has a charge Q. A particle carrying a charge q is placed a distance 2R from the sphere. Find the potential at point A located a distance R/2 from the center of the sphere on the line connecting the center of the sphere and particle q. Note...

Homework Statement A conducting spherical shell has inner radius a, outer radius b, and has a +Q point charge at the center. A charge of -Q is put on the conductor. a) What is the charge on the inner and outer surface of the shell? b) What is the electric field everywhere? c) What...

Wrote my question up in Latex Update: I have corrected the mistake when I stated the "textbook" version of the equation that the problem requires to be used. I have reposted the pdf with the same name.

The question is: a conducting spherical shell of radius a rotates about the z axis with angular velocity ω, in a uniform magnetic field B= B_{0}\hat{z} . Find an expression for the EMF developed between: i) the north pole and the equator (2 marks); ii) the north pole and the south pole (1...

Homework Statement A metal sphere with radius a is supported on an insulating stand at the center of a hollow, metal spherical shell with radius b. There is charge +Q on the inner sphere and charge -Q on the outer shell. Take the potential V to be zero at infinite separation. Calculate...

Homework Statement A conducting spherical shell is divided into upper and lower halves with a narrow insulating ring between them. The top half is at 10V and the bottom half is at -10V. Write down the appropriate expansion for Φ and use symmetry and the expected behavior at the origin to...

My class hasn't delved into Gauss's Law much besides describing conductors at electrostatic equilibrium to have no net electric field or force within itself. For the picture, the question is: What are the magnitudes of the electric fields at: 1) r = a 2) r = 3/2 a 3) r = b...

Homework Statement Consider a spherical shell with inner radius r1=0.30 m and outer radius r2=1.00 m. The hollow inside the shell contains no charge; and charge is distributed on the inside surface of the shell and within the shell itself, such that the electrical field inside the shell itself...

Just a quick general question in applying Gauss's law. Not exactly homework, more a general question so I can understand my other homeworks better. I have a spherical shell with inner radius R_1 and outer radius R_2 and a point charge Q in its center. It is NOT a conducting sphere. In the...

Hey. There's one thing I've always been wondering about when it comes to deriving the expression for the moment of inertia of a spherical shell. Namely, why is the length of the infinitesimal cylinder used in the derivations (like here ) equal to ##R d \theta##, instead of ##R d \theta...

In chapter 5, magnetostatics, of Griffiths' Introduction to Electrodynamics (third edition), there's a problem in the back of the chapter that asks you to calculate the force of attraction between the northern and southern hemispheres of a spinning charged spherical shell. The problem in its...

Homework Statement A hollow conducting spherical shell has radii of .80m and 1.20m. The sphere carries a net charge of -500 nC. A stationary point charge of +300 nC is present at the center origin. Calculate the electric field at points: a) 0.30m b) 1.00m c) 1.50m I have attached the image...

Homework Statement (From Physics for Scientists and Engineers, 7E, Serway-Jewett Chapter 25 Q11) (i) A metallic sphere A of radius 1 cm is several centimeters away from a metallic spherical shell B of radius 2 cm. Charge 450 nC is placed on A, with no charge on B or anywhere nearby. Next...

So i can see by symmetry arguments why The electric field inside a uniformly charged spherical shell would be zero inside. But what about a non uniformly charged spherical shell. Say most of the charge is located on one side, why is the electric field still zero? I can see that the flux...

A spherical shell and a conducting sphere each of radius R are charged to maximum potential. Which of the two has more charge? My attempt: Since in a conductor, no charge can reside inside the conductor so all charge is on the surface of the conductor just like the spherical shell. Now ...

Homework Statement Metal sphere of radius R1 is surrounded by a concentric metal shell of inner radius R2 and outer radius R3. The dielectric is air. Calculate coefficients of capacitance for the given setup. Homework Equations Picture of the problem: The Attempt at a Solution...

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...

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.

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...

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 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...

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...

If I have a +5 nC charge on the inside of the shell, the inside surface would be -5nC, the outside would be +5 nC and between those surfaces there would a 0 charge, right? So just to make sure I have it all straight, the INSIDE of the shell would actually be 0 because the INNER SURFACE is -5...

1. Homework Statement A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of...

Homework Statement A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the...

Homework Statement Consider a spherical shell with radius R and surface charge density σ = σ0 cosθ (a) What is the total charge carried by the shell? (b) Please evaluate the charge carried by the upper hemisphere, in terms of σ0. Homework Equations Q=∫σ0 cosθ da The...

Homework Statement A small charged ball lies within the hollow of a metallic spherical shell of radius R. Here, for three situations, are the net charges on the ball and shell, respectively: 1 +4q, 0 2 -6q, +10q 3 +16q, -12q (a) Rank the situations according to the charge on the...

Homework Statement An insulated spherical conductor of radius R1 carries a charge Q. A second conducting sphere of radius R2 and initially uncharged is then connected to the first by a long conducting wire. (a) After the connection, what can you say about the electric potential of each...

Homework Statement The inner radius of a spherical insulating shell is c=14.6 cm, and the outer radius is d=15.7 cm. The shell carries a charge of q=1451 E−8 C, distributed uniformly through its volume. The goal of this problem is to determine the potential at the center of the shell (r=0)...

Homework Statement A non-conducting spherical shell is uniformly charged. The electrostatic potential \phi at the centre of the sphere is \phi1 = 200V The potential at distance r = 50cm from the centre is \phi2 = 40V Find the radius of sphere: a Homework Equations I seem to have...

Just wondering if we have a non-conducting spherical shell which is uniformly charged and we know the potential at the centre and the potential at some radius how can we find the radius of the shell?