What is Spherical shell: Definition and 213 Discussions
In geometry, a spherical shell is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric spheres of differing radii.
The electric field inside a charged spherical shell moving inertially is, per Gauss's law, zero.
If the spherical shell is accelerated, the field inside is not zero anymore, but it gains a non-null component along the direction of the acceleration, as mentioned, for example, in this paper.
The...
In general relativity, rotation of mass gives rise to framedraging effects, just like linear motion does, because of the off-diagonal components in the mass-energy-momentum tensor. So around Bonnor beams there is framedragging, as well around a rotating mass.
Now imagine a spherical rotating...
First draw a gaussian shape outside of the sphere (a larger sphere) with radius R. The total charge from the (inner) sphere will be:
$$Q = \sigma A$$
$$A = 4\pi r^2$$
$$Q = \sigma 4\pi r^2$$
Use Gauss's Law to derive electric field magnitude
$$\oint_{}^{} E \cdot dA = \frac{q_e}{\epsilon_o}$$...
A known result is that the average field inside a sphere due to all the charges inside the sphere itself is proportional to the dipole momentum of the charge distribution (see, for example, here).
I wonder whether the same result can be applied in the case of a spherical shell of non-uniform...
My approach is thus: the shell will have induced charges if it's conducting resulting in E at the centre of shell(though flux at centre will be 0). For non conducting spheres there can be no induction only polarization of dipoles, therefore the E field at centre will remain 0. Is my approach...
When I look at the relevant equations, then there is no mention of field for a point on the surface of the shell, so it gets confusing. On the other hand, I feel the radial E will get stronger as we approach the surface of shell and magnitude of E will approach infinity.
The only explanation that I have seen in textbooks is that since the outer spherical shell is symmetrical relative to internal charged spherical shell so field every where on the outer shell is same in magnitude at every point on it.
I can understand that electric field needs to be...
So here was my first go around at it:
At first it made sense in my head but don't think my process is correct. Then i noticed the example in the book:
I guess the reasoning isn't 100% there in my head and if i don't have an actual σ, how will i cancel out any legendre polynomials due to...
I don't understand how this can be solved.
The official solution was:
F=\sigma*T^4
E=F*4\pi R^2*60*60
This doesn't make sense to me, as it seems to imply that the energy that the black body radiates depends on the radius of the shell. For a very large shell the body will reflect...
So for the Gaussian theorem we know that $$ \frac{Q}{e} = \vec E \cdot \vec S $$ Q's value is known so we don't need to express it as $$Q=(4/3)\pi*(R_2 ^3-R_1 ^3)*d$$ where d is the density of the charge in the volume. I've expressed the surface $$S=4\pi*x^2$$ where x is the distance of a point...
Homework statement:
Find the electric field a distance z from the center of a spherical shell of radius R that carries a uniform charge density σ.
Relevant Equations: Gauss' Law
$$\vec{E}=k\int\frac{\sigma}{r^2}\hat{r}da$$
My Attempt:
By using the spherical symmetry, it is fairly obvious...
a. This solution is i can consider the charge Q as a point charge and the electric potential at a distance r is
## V = Q/(4πεοr)##
b. This is where the confusion starts again when r2>r>r1, my answer
##
V = ρ*4*π(r^3 - r_1^3)/(3*4πεοr) \\
V = ρ*(r^3-r_1^3)/3εοr; ##
I know i am making some...
Homework Statement: Derive the formula for the moment of inertia of a thin spherical shell using spherical coordinates and multiple integrals.
Homework Equations: Moment of Intertia is (2MR^2)/3
I = (2MR^2)/3
Hi, been a while since I last asked here something.
I am restudying electrostatics right now, and I am facing difficulties in the following question:
My attempt:
I tried to use Gauss' law, what I got is the equation in the capture but that doesn't lead me anywhere as I am unable to find a...
Hi! I need help with this problem. I tried to solve it by saying that it would be the same as the field of a the spherical shell alone plus the field of a point charge -q at A or B. For the field of the spherical shell I got ##E_1=\frac{q}{a\pi\epsilon_0 R^2}=\frac{\sigma}{\epsilon_0}## and for...
Hi! I need help with this problem.
When the outer shell is grouded, its potential goes to zero, ##V_2=0## and so does it charge, right? ##-Q=0##. So the field would be the one produced by the inner shell ##E=\frac{Q}{4\pi\epsilon_0 R_1^2}##.
When the inner shell is grounded, I think that...
The textbook says
' A conducting sphere shell with radius R is charged until the magnitude of the electric field just outside its surface is E. Then the surface charge density is σ = ϵ0 * E. '
The textbook does show why. Can anybody explain for me?
Hi! I need help with this problem. I tried to do it the way you can see in the picture. I then has this:
##dE_z=dE\cdot \cos\theta## thus ##dE_z=\frac{\sigma dA}{4\pi\epsilon_0}\cos\theta=\frac{\sigma 2\pi L^2\sin\theta d\theta}{4\pi\epsilon_0 L^2}\cos\theta##.
Then I integrated and ended up...
Given that L is the luminosity of a single star and there are n stars evenly distributed throughout this thin spherical shell of radius r with thickness dr, what is the total intensity from this shell of stars?
My calculations were as follows: Intensity is the power per unit area per steradian...
If a charge is put inside a spherical shell, why is the electric field outside the shell independent of the location of the charge? Gauss's law could find that the net flux is independent, but not each individual field?
Is this something about the surface charge density being independent of...
I am modeling some dynamical system and I came across integral that I don't know how to solve. I need to integrate vector function f=-xj+yi (i and j are unit vectors of Cartesian coordinate system).
I need to integrate this function over a part of spherical shell of radius R. This part is...
Homework Statement
Consider a spherical shell with uniform charge density ρ.
The shell is drawn as a donut with inner (R1) and outer (R2) radii.
Let r measure the distance from the center of the spherical shell, what is the electric field at r>R2, R1<r<R2, and r<R1.
I am working on the r > R2...
Homework Statement
Given there is a conducting sphere which has a charge q on it. A plane cuts the sphere into 2 form a distance r from centre. How can we calculate the electrostatic force on one part on either side of the plane due ro the other part?
Homework EquationsThe Attempt at a...
Homework Statement
From Griffiths Third Edition: "Introduction to Electrodynamics" p.p. 81 ex. 2.6
"Find the potential inside and outside a spherical shell of radius R, which carries a uniform surface charge. Set the reference point at infinity.
Homework Equations
V(r) = -∫E⋅dl
The...
The electric field experienced by the points on the surface of the shell is put out as
KQ/R^2
where Q is charge on shell and R is radius of shell...
But the gaussian surface corresponding to the case intersects the sphere, which means there are non-infinitesimal charge quantity sitting on the...
Homework Statement
How much work is required to squeeze a uniformly charged spherical shell from a radius of ##r## to a radius of ##r−dr##, if
(a) the total charge q is a constant,
(b) the sphere is kept at a constant potential, e.g. grounded.
(c) Are the answers the same or different...
Homework Statement
Find the total electric charge in a spherical shell between radii a and 3a when the charge density is:
ρ(r)=D(4a-r)
Where D is a constant and r is the modulus of the position vector r measured from the centre of the sphere
Homework Equations
Q=ρV
Volume of a sphere =...
Homework Statement
A spherical shell of radius R has a surface charge distribution σ = k sinφ.
Calculate the dipole moment of the spherical shell.
Homework Equations
P[/B]' = ∫r' σ(r') da'
The Attempt at a Solution
So I believe my dipole will be directed along the y axis, as the function...
Homework Statement
Figure 23-30 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 µC/m2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density -3.8 µC/m2 on its outer surface and radius 2.0 cm. The shell centers...
Homework Statement
A conducting sphere, radius R, charged with Q is inside a conducting shell (2R<r<3R) with charge 2Q. Find the electric potential and the energy.
Homework Equations
\Phi =-\int_{r_1}^{r_2} \vec{E}\cdot\vec{dl}
U=\int_{V}E^2dV
The Attempt at a Solution
I think i got it...
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
a thick spherical shell carries charge density k/r^2 a<r<b
find E in the three regions r<a a<r<b b<r
Homework Equations
E dot da = Q/ε
The Attempt at a Solution
I can't understand why, when integrating, they choose for
ii to integrate between a and r,
iii and the between a...
Homework Statement
A 10-nC point charge is located at the center of a thin spherical shell of radius 8.0 cm carrying -20 nC distributed uniformly over its surface.
What is the magnitude of the electric field 2.0 cm from the point charge?
Homework Equations
E = kq1q2/r^2
The Attempt at a...
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...
Homework Statement
What is the gravitational potential both inside and outside a spherical shell of inner radius b and outer radius a?
Homework Equations
φ = ∫g⋅da = -4πGMencl
g = d∅/dr in the r hat direction
The Attempt at a Solution
I can get as far as getting the gravitational field for...
Homework Statement
Suppose the nonconducting sphere of Example 22-4 has a spherical cavity of radius r1 centered at the sphere's center (see the figure). Assuming the charge Q is distributed uniformly in the "shell" (between r = r1 and r = r0), determine the electric field as a function of r...
Homework Statement
Lets say, there is a non-uniform charge distribution, given as in a spherical shell that has a cavity with radius a and the radius b to the outer surface. I am wondering if the field is discontinuous just on the surface of this sphere.
Homework Equations...
Is there a potential on the inner surface of a charged spherical shell?
I know that there is no electric field on the inner surface, as shown by Gauss's Law, but that isn't enough information to say that the potential (V) there is zero since E = dV/dr, so V could be a nonzero constant.
If...
I know that gravitational potential due to uniform sherical shell at a point outside the shell is equivalent to the potential due to particle of same mass situated at the centre and got proof here http://m.sparknotes.com/physics/gravitation/potential/section3.rhtml. But I was looking for more...
Homework Statement
In the figure a nonconducting spherical shell of inner radius a = 2.07 cm and outer radius b = 2.51 cm has (within its thickness) a positive volume charge density ρ = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball of...
Homework Statement
An insulator is in the shape of a spherical shell. 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 C (1 C = 10-6 C). You may assume that the charge is distributed uniformly throughout the volume of the...
Homework Statement
Hi everybody! I would like to clear up some doubts I have about my electromagnetism homework:
A positive point charge ##q## is placed in the center of an ideal conducting electrically neutral spherical shell, as shown in the attached picture.
a) Calculate the electrical...
I am asked to find the total gravitational energy of a hollow sphere using the fact that the field energy density is given by ##u_g = \frac{-1}{8\pi G}g^2##.
Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give...
Homework Statement
A) [/B]Consider a hollow sphere of uniform density with an outer radius R and inner radius \alpha R, where 0\leq\alpha\leq1. Calculate its moment of inertia.
B) Take the limit as \lim_{\alpha\to1} to determine the moment of inertia of a thin spherical shell.
Homework...
1. Calculate the work that must be done on charges brought from infinity to charge a spherical shell of radius
R = 0.100 m to a total charge of Q = 125 μC.2. V = k_e\int{\frac{dq}{r}} \triangle V = - \int{E \cdot ds} W = q\triangle V 3. I started with assuming the spherical shell produces an...
Homework Statement
There are three point charges inside a conducting spherical shell of radius R. One of them of charge -2q is in the origin and the other two with charge q are in z=d and z=-d. Find the potential inside the sphere!
Homework Equations
##\nabla^2\phi=4\pi \rho##
3. The attempt...
Hello all,
Guys in my textbook they state that on a point mass at point outside spherical shell of uniform density, the gravitational force is just as if the entire mass of the shell is concentrated at the Centre of shell.
The text also states, the force of attraction due to a hollow...
Edit: Forgot to type "stumped" at the end of the title
1. Homework Statement
Instead of typing it out, a link to a scanned document of the problem is here: http://imgur.com/Be3jSLp.
Homework Equations
The equations to use are stated in the problem here: http://imgur.com/Be3jSLp
The Attempt...