What is Gaussian surface: Definition and 54 Discussions
A Gaussian surface (sometimes abbreviated as G.S.) is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field. It is an arbitrary closed surface S = ∂V (the boundary of a 3-dimensional region V) used in conjunction with Gauss's law for the corresponding field (Gauss's law, Gauss's law for magnetism, or Gauss's law for gravity) by performing a surface integral, in order to calculate the total amount of the source quantity enclosed; e.g., amount of gravitational mass as the source of the gravitational field or amount of electric charge as the source of the electrostatic field, or vice versa: calculate the fields for the source distribution.
For concreteness, the electric field is considered in this article, as this is the most frequent type of field the surface concept is used for.
Gaussian surfaces are usually carefully chosen to exploit symmetries of a situation to simplify the calculation of the surface integral. If the Gaussian surface is chosen such that for every point on the surface the component of the electric field along the normal vector is constant, then the calculation will not require difficult integration as the constants which arise can be taken out of the integral. It is defined as the closed surface in three dimensional space by which the flux of vector field be calculated.
If I have a point charge q right outside of a gaussian surface, it makes sense that the flux is zero inside the surface because the electric field going in equals the electric field going out. However, how would the electric field be zero inside? Wouldn't it just take on the electric field of...
There's something I need to confirm about Gauss' law. If I have to determine the electric field at point P due to charge +q, I take a Gaussian sphere enclosing the charge with the point on the surface of the sphere. So Gauss law doesn't care about the charge +Q because the flux do to this charge...
Homework Statement
A metal sphere of radius a is surrounded by a metal shell of inner radius b and outer radius R, as shown in the diagram below. The flux through a spherical Gaussian surface located between a and b is 1.20Q/εo and the flux through a spherical Gaussian surface just outside R is...
Homework Statement
[/B]Homework Equations
V= kq/r.[/B]The Attempt at a Solution
For 8-8, I do not really know how to approach it.
For 8-14 , I think that q2=-q1 and q3=q1+q2.
I can now use V=kq/r and then find the equations for r>R3 , r=R3 , R2<r<R3 , r=R2 and R1<r<R2 and then graph...
Homework Statement
What I basically want to do is to prove Gauss Law with a cylinder perpendicular to an infinite charged wire (I know I can do this simple, but I want to do it this way)
This is what I have done so far:
Homework Equations
$$\Phi=\int \frac{dq}{4\pi \varepsilon_0 r^2} \hat{r}...
Homework Statement
A thin spherical shell with radius R1 = 2.00 cm is concentric with a larger thin spherical shell with radius 6.00 cm . Both shells are made of insulating material. The smaller shell has charge q1=+6.00nC distributed uniformly over its surface, and the larger shell has charge...
Homework Statement
Two concentric cylindrical conducting shells of length L are separated by a vacuum. The inner shell has surface charge density +σ and radius ra. The outer shell has radius rb. Using Gauss’ Law, as a function of radius r find: The direction and magnitude of electric field...
Why doesn't the flux through a Gaussian surface change, when the shape is changed? (while keeping the net charge inside it the same)
Flux is the dot product of electric field and surface area, so wouldn't it change if surface area is changed?
Homework Statement
An infinitely long, cylindrical, conducting shell of inner radius b and outer radius c has a total charge Q. A line of uniform charge distribution Λ is placed along the axis of the shell. Using Gauss's Law and justifying each step, determine. A) The Electric Field for r>a...
Hello
If we have a gaussian surface that is placed in a uniform electric field E and encloses 0 charge, what would the E-field at the gaussian surface be? I have assumed the gaussian surface to be cubic surface, and then I have found from Gauss's law that the electric field is zero at the...
Homework Statement
a) 21.4-nC of charge is placed on a 4.8-m long steel tube with a d = 5.9-cm diameter. What is the magnitude of the electric field as a radial distance of r = d / 3?
b) What is the magnitude of the electric field as a radial distance of r = 20 d?
I was able to determine the...
Homework Statement
The electric field has been measured to be horizontal and to the right everywhere on the closed box shown in the figure. All over the left side of the box E1 = 80 V/m, and all over the right, slanting, side of the box E2 = 400 V/m. On the top the average field is E3 = 260...
Homework Statement
I'm trying to calculate the electric field through two oppositely charged plates with the same magnitude:
http://imgur.com/uXCQqtW
Homework Equations
Flux = ∫E⋅dA = Qenclosed/ε0
The Attempt at a Solution
I understand how the electric field is calculated using S1 and S4...
1. We have two positive point charges (+q) at a distance from each other
2. Goal is to Find electric field at point A halfway between the point charges
3.By logic and summation of fields we should get ZERO
4. But how would I use a gaussian surface (sphere i assume ) to prove at point A...
Homework Statement
I understand why, using Gauss's law, the net charge within a conductor should be zero at any point. However, when I try making a Gaussian surface that is so small so as to enclose a single proton, I cannot see why the enclosed charge should be zero for that situation as...
So the problem statement is:
A conducting solid sphere (R = 0.167 m, q = 6.63·10–6 C) is shown in the figure. Using Gauss’s Law and two different Gaussian surfaces, determine the electric field (magnitude and direction) at point A, which is 0.00000100 m outside the conducting sphere. (Hint: One...
Homework Statement
An uncharged spherical thin metallic shell has a point charge q at its center. Find expressions for the electric field
Inside the shell
Outside the shell
has the shell any effect on the field due to q?
has the presence of q any effect on the shell?
if a second point charge...
Homework Statement
in the following figure, the dashed line denotes a Gaussian surface
enclosing part of a distribution of four positive charges.
a) which charges contribute to the electric field at P?
b) is the value of the flux though the surface, calculated using
only the...
Homework Statement
The problem was to calculate the electric field inside an infinite length cylinder (with radius R) with a non uniform charge density. The charge density depended on r. Its easy enough to solve using a gaussian cylinder with r less than R. But what if I wanted to complicate...
1. A solid dielectric sphere of radius 10 cm has an electric charge uniformly distributed throughout its volume. The electric field at 5 cm from the center of the sphere is 8.6 x 10^4 N/C, pointing radially outward. Calculate the magnitude and direction of the electric field at a point 15 cm...
Consider a point charge q at the vertex of an arbitrary cube. If asked to consider the flux the cube experiences, q/8epsilon seems a natural answer, by constructing seven more such cubes to create an overall cube of 8 times the volume with q at its center.
But, this doesn't make sense to me...
1 Why do we choose a spherical surface as gaussian surface for a point charge to calculate electric field?
In my view, the reason may be
i. If we take the point charge at centre, each point of spherical surface will be at same distance from the...
The field makes an angle θ with side 1 and the area of each face is A. In symbolic form, find the electric flux through (a) face 1, (b) face 2, (c) face 3, (d) face 4 and (e) top and bottom.
My professor got:
a=EAcosθ
b=-EAsinθ
c=-EAcosθ
d=EAsinθ
e= 0
I understant why e=0 but for the...
Homework Statement
a cylindrical solid of charge q, radius R, and length H. The Gaussian surface S is a cylindrical shell of radius r and length h, with r < R. Determine the net electric flux given that q = -48Q, R = 4L, H = 3L, r = 2L, and h = 2L (type the integer value, along with the sign...
Homework Statement
Consider a uniformly charged sphere (an insulating sphere of radius R,) and a spherical Gaussian surface with radius R/2 concentric to the sphere. What is the total flux flowing through the Gaussian surface?
Homework Equations
Vsphere= (4∏R^3)/3
Asphere= 4∏R^2
Gauss' Law...
Homework Statement
A point charge of negative polarity is located at the centre of a cubic Gaussian surface with edges of length ##0.5m##.
Calculate the electric flux through one of the faces of the surface.
What would happen if the charge was moved 10cm to the right?
Homework Equations...
Homework Statement
Suppose there is a uniformly charged cube with known side length. I then imagine a larger, closed cube surface surrounding it. This larger cube has double the side length and is symmetrical to the smaller cube.
Is is practical to use this Gaussian surface to compute the...
If I have an oscillating charge inside of a sphere, will the integral of E(t), where t=proper time of the sphere, over the sphere's surface area result in a value of electric flux equal to the value of the charge?
If I have a spread of electrical charges contained inside a Gaussian surface, and if I cause those electrical charges to move at relativistic speeds, the electric fields of those charges should be subject to relativistic contraction. What happens then to electric flux that cuts through that...
Homework Statement
Say you have a nonconducting spherical shell. A is the inner radius and B is the outer radius. If you wanted to set up an integral to find the flux, would the gaussian surface include B, or be just inside it? That is, would the limits of integration go from A to B?
If...
Homework Statement
A uniformly charged, straight filament 7.00 m in length has a total positive charge of 2.00 \muC. An uncharged cardboard cylinder 2.00 cm in length and 10.0 cm in radius surrounds the filament at its center, with the filament as the axis of the cylinder. Using reasonable...
Homework Statement
A metal sphere of radius a is surrounded by a metal shell of inner radius b and outer radius R, as shown in the diagram below. The flux through a spherical Gaussian surface located between a and b is 1.20Q/εo and the flux through a spherical Gaussian surface just outside R...
Homework Statement
A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per...
So I'm pretty sure I have the right answer I just want to make sure I am getting the idea.
There is a large solid copper cube. At the center of the cube there is a hollow sphere of radius a. At the center of the hollow sphere there is a charge Q.
What is the total charge induced on the...
Hi all, I need your help with a question. Here goes,
Homework Statement
There is a hollow conducting sphere with a uniform surface charge density of +\sigma. A charge -q, is placed inside the cavity of the hollow sphere. What is the electric flux through a spherical surface just inside...
Hey there, just had a question about Gauss' law, should be relativity simple however the explanation we were given was quite poor and only seems to apply well to the examples we were given. (This isn't homework).
I (think I ) know the equation for Gauss' Law and what it means, that basically...
i would really appreciate if someone could help me out with this one. i m preparing for an exam and this question is a question from papers of previous years and its bugging me because it seems very specific in that i can't seem to find anything like it in textbooks.
what i m mainly stuck on...
i would really appreciate if someone could help me out with this one. i m preparing for an exam and this question is a question from papers of previous years and its bugging me because it seems very specific in that i can't seem to find anything like it in textbooks.
what i m mainly stuck on...
Hello all, new here.
In the past few weeks, I have been trying to gain a basic understanding of classical electricity and magnetism through the fantastic lectures at http://ocw.mit.edu, specifically the physics course...
Gauss' Law only figures out the the total charge enclosed by the Gaussian surface and on it, I treid this in a few cases where charges were placed only inside the surface, and my answers were correct.
But, when I tried imagining how to do this if there were charges present outside...
Homework Statement
A particle charge of q is placed at one corner of a Gaussian cube. What multiple of q/\epsilon_0 gives the flux though each cube face not making up that corner?
The solution is amazing - stack up eight cubes around the corner and find the flux through each individual cube...
Homework Statement
In the case of calculating electric field due to an infinitely long line charge, we assume cylinder to be a gaussian surface and electric field and small area element of the cylinder acts along the same direction at the curved surface and they act perpendicular direction at...
Homework Statement
Consider the uniformly charged sphere with radius R. Q is the total charge inside the sphere. Find the total flux passing through the Gaussian surface (spherical shell) with radius r. (r<R)
Homework Equations
I I tried solving for the Electric Flux by simply...
In the figure below, the charge on a neutral isolated conductor is separated by a nearby positively charged rod. What is the net flux through each of the five Gaussian surfaces shown in cross section? Assume that the charges enclosed by S1, S2, and S3 are equal in magnitude.
Surface 1...
Homework Statement
A long cylindrical insulator has a uniformcharge density of 1.46uC/m3 and a radius of 6cm.a-What is the electric field inside the insulator at a distance of 2cm and 12cm? Answer should be in N/C.
b-How much work must you do to bring a q=0.086uC test charge from 12cm to 2cm...
Hi,
From what I understand the proof of Gauss' law applies only to finite surfaces.
Can anyone give an example of a charge distribution and an infinite Gaussian surface, where the total flux on it is not proportional to the enclosed charge?
Thanks!
Homework Statement
Can someone please explain what use gaussian surfaces have, in really simple terms?
I don't really understnd the point of wrapping an imaginary surface around a charge, when we can just do the calcs without the imaginary surface.
Also if there are preset gaussian surfaces...
For the following Eo is epsillon zero
Homework Statement
41. A solid nonconducting spere of radius R has a uniform charge distribution of volume charge density p = kr/R where k is constant and r is the distance from the center. Show the (a) the total charge on the sphere is Q =...