What is Gauss's law: Definition and 380 Discussions
In physics and electromagnetism , Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating to the distribution of electric charge to the resulting electric field. In its integral form, it states that the flux of the electric field out of an arbitrary closed surface is proportional to the electric charge enclosed by the surface, irrespective of how that charge is distributed. Even though the law alone is insufficient to determine the electric field across a surface enclosing any charge distribution, this may be possible in cases where symmetry mandates uniformity of the field. Where no such symmetry exists, Gauss's law can be used in its differential form, which states that the divergence of the electric field is proportional to the local density of charge.
The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1813, both in the context of the attraction of ellipsoids. It is one of Maxwell's four equations, which forms the basis of classical electrodynamics. Gauss's law can be used to derive Coulomb's law, and vice versa.
Homework Statement
The figure shows a portion of an infinitely long, concentric cable in cross section. The inner conductor carries a charge of 5.1 nC/m and the outer conductor is uncharged.
What is the electric field 1.9 cm from the central axis? The permittivity of free space is 8.85419e-12...
Homework Statement
Calculate E inside and outside an infinite cylinder of uniform volume charge density using the differential form of Gauss's law.
Homework Equations
\nabla E = \frac{p}{e0}
p = charge density
Divergence in cylindrical polars:
The Attempt at a Solution...
Four closed surfaces, S1 through S4, together with the charges -2Q, Q, and -Q are sketched in the figure below. (The colored lines are the intersections of the surfaces with the page.) Find the electric flux through each surface. (Use Q for the charge Q and epsilon_0 for 0.)
(Picture Attached)...
Can't find the error I made... Rudimentary problem i know but i can't find where my mistake is...
Homework Statement
A nonconducting sphere is made of two layers. The innermost section has a radius of 6.0 cm and a uniform charge density of -5.0 C/m3. The outer layer has a uniform charge...
Homework Statement
Suppose that the inner cylinder of the figure below is made of nonconducting material and carries a volume charge distribution given by ρ(R) = C/R, where C = 301 nC/m2. The outer cylinder is metallic and both cylinders are infinitely long.
a.Find the charge per unit...
Homework Statement
A point charge Q is located on the axis of a disk of radius R at a distance b from the plane of the disk (Fig. below left). Show that if one fourth of the electric flux from the charge passes through the disk, then R = sqrt(3)b.
PLEASE SEE ATTACHED WORD DOCUMENT FOR...
I've stumbled upon a website that claims that he has created a hollow spherical electromagnet that could contain plasma.
http://justodians.org/SphericalMagnet/PatentApp.htm
I don't know the credibility of his claims but I would appreciate an analysis of his "invention". Does this device...
Homework Statement
A hollow spherical conducting shell has a uniformly distributed total surface charge density of -15\muC/m^2. It's outer surface has a radius R1=0.25m. Its inner radius is R2=0.15 m. A point charge, Q= -6.0\muC, is placed at the center of the spherical charge. Determine the...
Ok so background story, everyone failed an exam in my physics 2 class, so as a way to gain points we had to complete a packet of 35 physics2 problems, and i am having issues with only 6 problems.
1. Does a charged particle in an electric field always move along a field line? if yes, explain; if...
Homework Statement
In a model of an atomic nucleus, the electric field is given by:
E = α r for r < a
where α is a constant and a is the radius of the nucleus.
Use the differential form of Gauss's Law to calculate the charge density ρ inside the nucleus.
2. The attempt at a...
Homework Statement
A small conducting spherical Shell (#1) with inner radius a and outter radius b is concentric with a larger conducting spherical shell (#2) with inner radius C and outter radius d. The inner shell has a total charge (-3Q), and outter shell has a charge ( +5 Q).
a) Use...
Hi guys. My question is related to proving Gauss's law by using Columb's law. Let start with a charge density \rho(\vec{r}) in R^3 . by Columb's law we have :
E(\vec{r})=\int{\frac{\rho(\vec{r'})d^3r'(\vec{r'}-\vec{r})}
{|\vec{r'}-\vec{r}|^3}}
suppose that domain of function \rho(\vec{r})...
[Solved] Gauss's Law Question
Well, I've been reading up on Resnick, and have reached the chapter on Gauss' Law.
He provides an example where he uses Gauss's Law to calculate the E field just outside a positively charged conductor (Arbitrary shape):
His reasoning was as follows:
We...
Homework Statement
The electric field between two square metal plates is 180 N/C. The plates are 1.0 m on a side and are separated by 3.0 cm, as in the figure. What is the charge on each plate? Neglect edge effects.
Homework Equations
i don't know how to make any fancy sybols sorry...
Im really having troubles understanding the divergence form of gauss's law. I have done research on it and am still not able to understand it. it sates that E=\rho/\epsilon or E=rho/epslom, so does that mean that the upside down triangle has no significance, ie does that mean i can simply solve...
Homework Statement
Homework Equations
\Phi = \int{\vec E \cdot d\vec A}= \frac{q_{enc}}{\epsilon_0}
The Attempt at a Solution
The positive plate is drawn to the left of the negative plate. If we draw a Gaussian surface around the inner edge of of the positive plate, we can see...
Homework Statement
Homework Equations
\Phi = \int{d\vec E \cdot d\vec A}
\Phi = \frac{q_{enc}}{\epsilon_0}
The Attempt at a Solution
I'm having a problem with this problem. I don't really understand the givens.
If we're dealing with thin-walled cylinders, we're dealing with...
It's evident that ampere's law is used to calculate the magnetic field produced by flowing charges. Can I use Gauss's Law to calculate the electric field produced by the flowing charges also?
I ask this question because in the middle of a solid conductor, there is a flow of charge. However...
Homework Statement
An insulating sphere with radius 0.120 m has 0.750 nC of charge uniformly distributed throughout its volume. The center of the sphere is 0.240 m above a large uniform sheet that has charge density -9.40 nC/m2. Find all points inside the sphere where the electric field is...
Homework Statement
So here's the question...
A cylindrical shell of radius 7.00 cm and length 240 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm radially outward from its axis (mesaured from the midpoint of the shell) is...
Homework Statement
https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2112/summer/homework/Ch-21-Gauss-Law/charged_sheet/sheet.gif
An infinite nonconducting sheet of charge, oriented perpendicular to the x-axis,passes through x = 0. It has area density σ1 = -3...
My physics textbook emphasizes that the electric field appearing in Gauss's law is the resultant electric field due to charges present both inside and outside the chosen closed surface , while the 'q' appearing in the law is only the charge contained within the surface. .This appears to follow...
Homework Statement
Gauss's Law states that the gravatational flux crossing a closed surface is -4piGM, where M is the mass inside the surface.
A Long straight cylinder has a radius R and is made of material of a constant density of p
Show that the gravatational field at a distance r from...
Homework Statement
Suppose a conducting spherical shell carries a charge of 3.00 nC and that a charge of -2 nC is at the center of the sphere. If the distance from the center to the inner shell is 2.00 m, and the distance from the center to the outer shell is 2.40 m, find the electric field...
Homework Statement
A point charge of strength q1 = -4 µC is located at the center of a thick, conducting spherical shell of inner radius a = 2 cm and outer radius b = 3 cm. The conducting shell has a net charge of q2 = 5 µC
(a) Calculate the surface charge densities on the inner (sa) and...
Electricity and Magnetism questions...Gauss's law, grounding..etc.
Alright so I am finally starting to understand the material, but I have a few questions.
1. An insulating spherical shell with an inner radius of 0.1cm and outer radius of 0.3 cm carries a total charge of 20nC. Use Gauss's law...
Homework Statement
An infinitely long line charge having a uniform charge per unit length \lambda lies a distance d from point O as shown. Determine the total electric flux through the surface of a sphere of radius R centered at O resulting from this line charge. Consider both cases, where...
Homework Statement
In the air over a particular region at an altitude of 500 m above the ground, the electric field is 120 N/C directed downward. At 600 m above the ground, the electric field is 100 N/C downward. What is the average volume charge density in the layer of air between these two...
Consider Gauss's law:
\oint \vec{E}\cdot d\vec{a} =\frac{Q_{enc}}{\epsilon_0} . Which of the following is true?
A. E Must be the electric field due to the enclosed charge
B. If q=0 then E=0 everywhere on the Gaussian surface
C. If the charge inside consists of an electric dipole, then the...
Homework Statement
A cylindrical shell of radius 7.00 cm and length 24.0 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Find (a) the...
Homework Statement
A nonconducting wall carries charge with a uniform denisty of 8.g µC/cm2. What is the electric field 7.00cm in front of the wall? Explain whether your result changes as the distance from the wall is varied.
Homework Equations
I'm still really new, I just...
I am having trouble understanding the concept of cylindrical symmetry in an infinitely long line.
Please picture a finite Gaussian cylinder enclosing a portion of the length of the line, parallel to the line.
My book states that there cannot be any component of E perpendicular to the...
Homework Statement
Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities \sigma1, \sigma2, \sigma3, & \sigma4 on their surfaces, as shown in the figure .
These surface charge densities have the values \sigma1= -6.00E-6 C/m^2, \sigma2=...
Homework Statement
A flat surface with area .14 m^2 lies in the x-y plane, in a uniform electric field given by E=5.1i +2.1j+3.5k kN/C.
A) Find the flux through the surface.
Homework Equations
Flux = E dot A (Vector math?)
The Attempt at a Solution
I believe this is the dot...
Homework Statement
a 240nC point charge is placed at the center of an uncharged spherical consucting shell 20cm in radius. A) What is the surface charge density on the outer surface of the shell? B) What is the electric field strength at the shell's outer surface?
Homework Equations
A)...
Homework Statement
A very long uniform line of charge has charge per unit length 4.8*10^-6 Coulomb/meter and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.4*106-6 coulomb/meter and is parallel to the x-axis at y=.400 meters. What is the net electric...
Homework Statement
Use Gauss’s law to determine a formula for the electric field outside (and far from the ends) of a long, uniformly charged cylinder of radius R and surface charge density σ C/m2.
Homework Equations
I suppose net electric flux = ErA = Q/e0
The Attempt at a...
Homework Statement
A long solid nonconducting cylinder has radius r = 0.65 meters. It has a uniform charge density of 3.7 C/m3. Consider a cylinderical container concentric with the charged cylinder, with radius R = 1.5 m, and length L = 2 m.
Calculate the flux through the barrel of the...
Homework Statement
We have solid ball of radius rb and charge density \rho.
I need to find the magnitude of electric field E(r) at a distance r < rb from the center of the ball and express my answer in terms of \rho, r, rb, and \epsilon 0.
Homework Equations
Gauss's Law
\int EA...
Hi there,
I have a question for you guys. It might sound stupid, but I don't get the material; my teacher can't teach! and your help is very appreciated
I am reading about Gauss's law where they come to the conclusion that flux=charge/Eo
as in this link...
Homework Statement
A spherically symmetric charge distribution produces the electric field E = (5000r^2) N/C, where r is in m.
a) What is the electric field strength at r = 20cm?
b) What is the electric flux through a 40cm diameter spherical surface that is concentric with the charge...
This question is regarding the application of Gauss's Law to find the electric field within given objects, etc. For example, the question asks you to find the electric field inside a charged sphere, but how do you know when to use little "r" and big "R" when it comes to the radius?
Here are...
Homework Statement
Well, here's the homework question:
A charge Q is located inside a rectangular box. The electric flux through each of the six surfaces of the box is: phi1=+1500Nm^2/C, phi2=+2200Nm^2/C, phi3=+4600Nm^2/C, phi4=-1800Nm^2/C, phi5=-3500Nm^2/C, and phi6=-3400Nm^2/C. What is...
I was thinking about gauss's law and ran into this contradiction.
Consider this situation in electrostatics. You have an infinite line of charge, uniform charge density [text]\lambda[/tex]. In cgs units, E at a distance r from the line of charge along the +y axis (assuming a left handed...
Hi there, I was reading the Serway's physics book and I don't understand this quiz neither the solution. I mean, if the solution is a, what's the difference with option b?
http://img140.imageshack.us/img140/6812/gaussslawud7.png
The "Quick Quiz" is in the chapter "Gauss's Law", under the...
Homework Statement
Consider the cross sections of two, very long, concentric, metallic, hollow cylinders placed in a vacuum. The small cylinder has inner radius A and outer radius B while the larger cylinder has inner radius 2A and outer radius 2B. Initially the small and big hollow...
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
A long thin wire carries a charge \lambda per unit length
a) Use Gauss's Law on a cylinder to find magnitude of the E-Field at a distance from the centre of the wire
b) Show that the electric field components (using cartesian coordinates) are of the form:
E_x =...
1. A thick spherical shell has an inner radius Rsub1 and outer radius Rsub2, and for Rsub1 is less than r which is less than Rsub2, a volume charge density rho=C/r^3, where C is a constant. Find Electric Field for r=3Rsub2
My problem here is determining the excess charge of the shell. So I...
Homework Statement
A long, thin straight wire w/ linear charge density lambda runs down the center of a thin, hollow metal cylinder of radius R. The cylinder has net linear charge density of 2lambda. Assume lambda is positive. Find an expression for the electric field strength inside the...