Spherical shell Definition and 213 Threads

What is the capacitance C of a capacitor that consists of two concentric spherical shells, the inner of radius r_{1} and the outer of radius r_{2}? What would the limit be if r_{2}-r_{1}<<r_{1}. What would happen if r_{2} goes to infinity (assume the potential there is zero)? Some equations...

Calculate the dipole moment of a spherical shell of radius 'a' whose surface charge density is σ=σ0(1+cos(θ)). The origin is at the center of the sphere. What I know: 1) p=∫r'*ρ*dV' I'm having trouble understanding how to transform this equation so that I can calculate the dipole moment...

1. A spherical shell of radius R has a constant surface charge density, sigma. It rotates about its diameter with angular speed, w. Find the magnitude of the magnetic moment of the rotating spherical shell. 2. Magnetic dipole moment u = NIA(normal vector) ; Torque = u X B; Spherical Volume...

Electrostatics: spherical shell [SOLVED] Homework Statement A point charge Q_1 is located in the centre of a spherical conducting shell with inner radius a and outer radius b. The shell has total charge Q_2. Determine the electrostatic field \vec{E} and the potential \phi everywhere in...

When working on homework problems having to do with voltage, there is often the stipulation that V=0 at infinite. If you are dealing with a spherical conductive shell with charge Q, the Electric Field E is equal to K*Q/R^2, where K is the vacuum permittivity constant and R is the radius of the...

Now, i am trying to prove that electric field inside spherical shell whose constant surface charge density \rho is zero. Usually, it is proved by using Gauss law (there is no charge enclosed inside gaussian surface so there is no electric field inside the sphere). But, whe i am trying to solve...

1. A thin spherical shell of radius 6.8 m has a total charge of 7.77 C distributed uniformly over its surface. Find the electric field E 10.4 m from the center of the shell. Answer in units of N/C. ke = 8.988 * 10^9 Nm^2/C^2 2. E = ke * (Q/r^2) 3. I did (8.988 * 10^9...

A non-conducting, spherical shell centered at the origin has radius r1 and total charge -Q, where Q is a positive value. (DO NOT ASSUME THE POTENTIAL AT INFINTIY IS ZERO!) http://i662.photobucket.com/albums/uu347/TwinGemini14/ELECpotential.gif 1) The electric potential just outside the...

Hello I have a conceptual question about the following. Suppose I have a spherical shell with charge density \sigma that is uniformly distributed throughout its surface. My shell has radius a. Then I cut a little circular piece of radius b with b << a. Then I know that my electric field at...

Homework Statement The inner radius of a spherical shell is 14.6 cm, and the outer radius is 15.2 cm. The shell carries a charge of 5.35 × 10-8 C, distributed uniformly though its volume. Sketch, for your own benefit, the graph of the potential for all values of r (the radial distance from the...

Homework Statement Find the electric field and potential inside and outside a hollow spherical shell (a \leq r \leq b) which carries a charge density proportional to the distance from the origin in the region, \rho=kr, for some constant k. Homework Equations The Attempt at a Solution I think...

what the energy spectrum to second order in the field strength for a spherical shell?

Homework Statement Consider a solid conducting sphere with a radius 0.7 cm and charge −7.3 pC on it. There is a conducting spherical shell concentric to the sphere. The shell has an inner radius 2.8 cm(with 2.8 cm > 0.7 cm) and outer radius 5 cm and a net charge 27.9 pC on the shell. Denote...

Homework Statement Consider a conducting spherical shell with inner radius 0.8 m and outer radius 1.3 m. There is a net charge 3 μC on the shell. At its center, within the hollow cavity, there is a point charge 3 μC. Determine the flux through the spherical Gaussian surface S, which has a...

Homework Statement Hey guys. I've been trying to solve this question using Gauss law but I can't think of a surface that can contain this thing. Is there another way to solve this? Thanks a lot. Homework Equations The Attempt at a Solution

Homework Statement Hey guys. I got this question: "Calculate the electric field of half a spherical shell with radius R and uniform surface charge density \sigma along its axis of symmetry above the shell." I guess I shell use Gauss law, the thing is that the Gauss surface will not be...

Assume that there is a spherical dielectric inside spherical shell. There is a vacuum between the dielectric and the shell. I found this configuration rather tricky. Any idea ? http://img117.imageshack.us/img117/5901/conductorly3.th.jpg...

A nonconducting spherical shell of inner radius a=2.00 cm and outer radius b = 2.40 cm has (withing its thickness) a positive charge density p = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball of charge q=45.0 fC is located at that...

Express the current density of a spherical shell of radius a, rotating with angular velocity omega, with surface charge density sigma Delta function will be denoted d(x). Spherical coordinates will be used I have concluded that for a given chunk (if we restrict to the 0<theta<pi/2...

1. A thin spherical shell of radius a has a total charge Q distributed uniformly over its surface. Find the electric field at points outside the shell and inside the shell 2. \intE dA = Q/\epsilon 3. THis is an example in my textbook, and it claims that: The calculation for...

Homework Statement Electric Charge is distributed over a thin spherical shell with a density which varies in proportion to the value of a single function P_l(cos \theta) at any point on the shell. Show, by using the expansions (2.26) and (2.27) and the orthongonality relations for the...

A grounded & conducting spherical shell of outer radius M and inner radius N has a point charge Q inside the shell at a distance r<M from center. Using method of images, find the potential inside the sphere. Could I just use the superposition of charge and point charge? \phi(r) =...

[solved] Potential inside (and outside) a charged spherical shell Homework Statement Use the integral (i) to determine the potential V(x) both inside and outside a uniformly charge spherical surface, with total charge Q and radius R. Homework Equations (i) V(\vec{x}) =...

hey, i have a question from an exam paper which isn't worded too nicely (most of the questions on the exam are worded in similar ways ) The way I've done it is to first put in my first shell of infintesimal charge and then treat it as a point charge. Then i treat the next shell as just a point...

How do I solve for the temperature at a certain time for conduction through a spherical shell? I have a shell 5 cm thick with a radius of 0.5m. I am starting with Q=KA(T2-T1)/L and I am completely lost as to where to go with it. Thanks!

Homework Statement An insulated spherical shell with its center in the origin and radius R has a surface charge density of \sigma(\theta)=\sigma_0\sin(\theta) when \theta is the angle from the z axis. Calculate the electrical field outside the shell at point z=R. Homework Equations...

Homework Statement A perfectly conducting spherical shell of radius 'a' rotates about the z-axis with angular velocity \omega in a uniform magnetic field \mathbf{B} = B_0 \hat{\mathbf{z}}. Calculate the emf developed between the "north pole" and the equator.Homework Equations The Attempt at a...

Question: I have a thick spherical shell (inner radius a and outer b) with charge density = kr^2. I need to find the field and potential at all points in space and calculate the energy. Is it possible to take the equation for the electric field of a solid sphere, and integrate from a to b? Or...

Hello everybody, this is my first post here. I need help with a task in General Relativity. ------- Given we have a spherical shell in 2-space of radius \rho. With the line element: ds^{2} = g_{ab} dx^{a}dx^{b} = \rho d \theta^{2} + \rho^2 sin^2(\theta) d \phi^2 (a,b \in 1,2) Then...

Homework Statement Figure 16.69 A thin spherical shell made of plastic carries a uniformly distributed negative charge -7e-10 coulombs (indicated as -Q1 in the diagram). Two large thin disks made of glass carry uniformly distributed positive and negative charges 1.7e-05 coulombs and...

Can anyone help me how to calculate the moment of inertia of a thin spherical shell? Thank you

Homework Statement An insulator in the shape of a spherical shell is shown. The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = +9 microC. You may assume that the charge is distributed uniformly throughout the volume of the...

What is the potential energy of a uniformly charged spherical shell; i think it is called the self energy of shell.

A hollow spherical shell with mass 2.10 rolls without slipping down a slope that makes an angle of 34.0 with the horizontal. Find the magnitude of the acceleration of the center of mass of the spherical shell. I understood that the friction force is normal to the slope and there is a...

Homework Statement Show that the moment of inertia of a uniform thin spherical shell of mass m and radius a about a diameter is 2/3 ma^2 Homework Equations Moment of inertia = Sum m x R^2 volume of sphere = 4/3 pi r^3 The Attempt at a Solution I think i have to integrate the...

A half spherical shell as seen in the picture. http://img219.imageshack.us/img219/3424/picnw3.th.jpg charged with surface density \sigma(\theta)=\sigma_{0}cos\theta Need to find the Electric field in center of the axis. As I see the direction of the electric field is the Z axis...

An insulating spherical shell of the external radius b and the internal radius a is charged uniformly with volume charge density p. What force F does it produce on a uniformly charged thin rod, as shown in figure2? Rod's total charge is Q and length 2a. The rod is arranged radially from the...

For the configuration shown in the figure below, suppose that a = 5.60 cm, b = 19.8 cm, and c = 27.9 cm. Furthermore, suppose that the electric field at a point 13.7 cm from the center is 3.44 x 10^3 N/C radially inward, while the electric field at a point 47.0 cm from the center is...

Homework Statement I'm well aware of how to compute the gravitational [electric] potential \Phi due to a spherical mass [charge] distribution of radius R by using Newton's theorems for spherical shells. However, how does one find an analytic expression for \Phi without invoking these theorems...

1) A shperical sheel has inner radius R_in and outer radius R_out. The shell contains total charge Q, uniformly distributed. The interior of the shell is empty of matter and charge. Find the electric field for (a)r>R_out, (b)r<R_in, and (c)R_in<r<R_out respectively. Then sketch a graph of E...

Homework Statement A solid conducting sphere of radius 2.00 cm has a charge 6.70 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge -3.50 µC. Find the electric field at the folowing radii from the center of...

Homework Statement Consider a thin spherical shell having surface charge density σ, and radius a as shown in the diagram (see attachment). Find, by integration over the sphere, the potential at a point P, a distance r fromthe centre of the sphere, for r > a. Using this result also find...

Homework Statement spherical shell with inner and outer radii a and b, and with temperatures of the inner and outer surfaces T_2 and T_1, the thermal conductivity of the shell is k, derive an equation for the total heat current through the shell Homework Equations...

Griffith's EM problem 3.28 A spherical shell of radius R has a surface charge \sigma = k \cos \theta a) Calculate the dipole moment of this charge distribution. i know that p = r' \sigma(r') da' but here sigma depends on theta would the dipole moment p then turn into p = \theta'...

A hollow spherical shell carries a charge density \rho = \frac{k}{r^2} in the region a<= r <= b. As in the figure Find the elctric field in these three regions i) r <a ii) a<r<b iii) r>b SOlution: for r<a it simple.. no exclosed charge for any gaussian sphere within that region...

A charge punctiform of Q= 12*10\exp-6 C is in the center of a spherical shell conductor charged negatively Q1= 6*10\exp-6 C, and of internal radius = 22 cm ad external=26 cm. Calculate the electric field and potential.

Gauss' law---thin spherical shell INTRODUCTION- hello, actually i had been doing some problems on gauss' law from H.C.Verma "concepts of physics". I'm continuously having problem with "wht's the field on the surface of a thin spherical, conducting shell? THE EXACT PROBLEM IS- "Consider the...

In fact, This is a question I caucalated in HW. But I still dun understand the answer. Any have the idea about this question? The problem is in this link http://web.mit.edu/8.07/www/probsets/PS6s.pdf The problem No.2

The question is: A conducting spherical shell of inner radius b and outer radius c is concentric with a small metal sphere of radius a < b. The metal sphere has a positive charge Q. The total charge on the conducting spherical shell is –Q. What is the potential of the metal sphere? I...

1] A square loop of wire, with sides of length 'a' lies in the first quadrant of the xy-plane, with one corner at the origin. In this region there is a non-uniform time-dependent magnetic field \vec B (y,t) = ky^3t^2\hat z. Find the induced emf in the loop.I applied the flux rule here...