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 spherical region a < r < b carries a charge per unit volume of \rho = A/r, where A is a constant. At the center (r = 0) of the enclosed cavity is a point charge q. What should be the value of A so that the electric field in the region a< r < b has constant magnitude...
Homework Statement
Hi all,
I'm having some difficulty with electric flux.
Does electric flux stay the same if you double the diameter of a circle assuming the electric field is uniform?
Any help would be much appreciated.
Thanks
Homework Equations
Electric flux= E.A...
Hi all,
I'm having some difficulty with electric flux.
Does electric flux stay the same if you double the diameter of a circle assuming the electric field is uniform?
Any help would be much appreciated.
Thanks
Homework Statement
Immediately outside a very long cylindrical wire of radius r1 = 1mm, the electric field is 40kV/m directed towards the wire's surface.
A hollow cylindrical metal tube with inner radius r2 = 3mm is now placed around the wire, to form a coaxial cable. What will be the charge...
So I was doing this one problem in which there is a sphere of radius r and charge density row and there is a spherical cavity inside it whose center is at a distance r2 from the center of the bigger sphere.
Now the question was what is the E field inside the cavity.
My first and long...
Homework Statement
Calculate the electric field at a point 2.00 cm perpendicular to the midpoint of a 1.94 m long thin wire carrying a total charge of 4.78 uC.
Hint: You could integrate BUT if the wire is very long compared to the distance from the wire to where you are calculating the...
Homework Statement
A pyramid with horizontal square base, 6.00 m on each side, and a height of 4.00 m is placed in a vertical electric field of 52.0 N/C. Calculate the total electric flux through the pyramid's slanted surfaces.
Homework Equations
Electric Flux = E dot dA
The...
So I'm trying to understand a couple things regarding this.
lets say we have a plate that's charged to Q. and we want to find the E field of a point .1 meters above the plate. when i looked at the solution, it never took the .1 meters into account when calculating the strength of the E...
A 10.0 gram piece of styrofoam carries a net charge of -0.700\muC and floats above the center of a large horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet?
Homework Equations
\Phi = E\intdA =...
Homework Statement
On a clear, sunny day, a vertical electrical field of about 116 N/C points down over flat ground. What is the surface charge density on the ground for these conditions?
Homework Equations
The Attempt at a Solution
116*8.83e-12= 1.0266e-9
I'm stuck on a problem trying to determine charge, and I'm hoping someone can help.
Suppose that a = 5.00 cm, b = 20.0 cm, and c = 25.0 cm. Furthermore, suppose that the electric field at a point 15.5 cm from the center is measured to be 3.70 *103 N/C radially inward while the electric field...
Homework Statement
Is there an analog to Gauss's theorem (sorry about the title) in 2D.
The reason is to develop the continuity equation in 2D.Homework Equations
In 3D it is.
\int_{S}{\bf A}. d{\bf S}=\int_{V}(\nabla . {\bf A})dV
(please forgive my latex. A and dS should be vectors).
The...
[SOLVED] Gauss's Law problem
Homework Statement
An infinite slab of charge parallel to the yz-plane has density p for -b < x < b, 0 otherwise. Find the electric field at all points.
The Attempt at a Solution
I am able to do the electric field outside the slab. But I am off by a factor of...
Could someone try and explain with the differential form means? I've only taken p to calculus 2 so I'm not really sure what divergence in the sense of this equation means. Also what is the difference in the two. I mean the integral form looks at an electric field and charge over a region, so...
Homework Statement
An infinitely wide conductor (shaded thing on top) is parallel to and at a distance d from an infinitely wide plane of charge (line on bottom) with surface charge density delta. What are the electric fields E_1 to E_4 in the regions 1 to 4?
1
-------------------------
2 /...
Homework Statement
I know that the electric flux through some solid is E\pi\\r^2. E is an outside electric field directed towards the solid.
Does that mean that there is a net charge of magnitude \epsilon E\pi\\r^2 inside the solid?
My idea is that the net charge is opposite of the entry...
[SOLVED] Gauss's Law and Flux
ok so i have the biggest question of all i tried solving the following problem:
55.3 million excess electrons are inside a closed surface. What is the net electric flux through the surface?
now i tried the following equations:
\Phi= E . A = Qin/\epsilon...
My textbook (high school level) derives an instance of Gauss's Law with Dielectric for the case in which the dielectric material fills the gap between a parallel-plate capacitor entirely.
So you get surface int (D dot Area-vector) = q, where D = (dielectric constant)(epsilon_0)(Electric...
Homework Statement
Gauss's Law is often given as:
\nabla \cdot \vec{E} = \rho/ \epsilon_0
However E is, in general a function of position, so the equation is really
\nabla \cdot \vec{E}(\vec{r}) = \rho(\vec{r}) /\epsilon_0
correct?
Homework Equations
The Attempt at a Solution
[SOLVED] Help needed with Gauss's Law and Net Flux
A cube of side l-55cm is placed in a uniform field E= 7.30 X10^3 N/C with edges parallel to the field lines.
a. what is the net flux through the cube?
b. what is the flux through each of its six faces?
Face 1 perpendicular to E (field...
Homework Statement
Find the Electric Field everywhere in space for an infinitely long slab in the x-y plane with thickness (t) and uniform volume charge density (rho).
Find the electric field if the sheet becomes a conductor.
The Attempt at a Solution
I know the E field above and...
I've been taught that in gauss's law, the charge that is used must be the net charge enclosed by a closed gaussian surface. If the charge is located on the surface of the gaussian surface (such as a particle charge) can we still use gauss's law? In other words, am I right in interpreting...
Homework Statement
What is the net electric flux through the the torus if a=-6 nC and b=60 nC ?
Homework Equations
Electric flux=Qin/E
The Attempt at a Solution
I solved with Qin being 6*10^-9 C as it is the charge inside and E0=8.85*10^-12. I got 678 for electric flux. But it...
From Coulomb's law, as the distance between a charged particle and another charged particle approaches zero, the electrostatic force between the two particles approaches infinite.
However, according to Gauss's Law, we know that for a uniformly charged sphere or spherical shell, the charge...
A sphere of radius 2a is made of nonconducting material that has a uniform volume charge density . (Assume that the material does not affect the electric field.) A spherical cavity of radius a is now removed from the sphere, as shown in Figure P19.62. Show that the electric field within the...
Homework Statement
Ok so I', having some problems with Gauss's law. I know what it is, but I still can't get the answers right.
A metallic sphere of diameter 2*10-2m has been given a charge of 2 nC. State Gauss's law. Use this to determine the electrical field at the surface of the...
The Ampere's Law is \nabla \times B = \mu J and Gauss's Law is \nabla \cdot E = \frac{1}{\epsilon} \rho
Since J is current density, is it right to say that, J = \frac{d}{dt} \rho in general?
I am abit confused, since I know that a current four-vector, (\rho , J) is similar to a...
Gauss's law may be used to derive Coulomb's law. I've never seen it done the other way around. Is this possible? Because I have not seen it, I infer that these forms are not logically equivalent.
Question:
http://web.ics.purdue.edu/~yeo/phys1.jpg
Formula: (Gauss's Law for Magnetism)
Line integral of[B dot nhat(perpendicular unit vector) * deltaA] = 0
The Attempt at a Solution
So, if there is a bar magnet inside, the side arrows are pointing in the wrong direction, so I ruled...
This question is giving me problems.
Consider Gauss's law: (integral) E.dA = qenc/(perm. free space). Which is true?
A. If q = 0, then E = 0 everywhere on the surface.
If there is no enclosed charge, there is no flux.. so no electric field, correct?
B. On the surface, E is everywhere...
Hey, I'm having some trouble solving for the dA portion of Guss's Law for a sphere as the Gaussian surface and a point charge on the inside.
According to my book, Integral(1dA) = 4(pi)r^2
So when I try to integrate it myself I get 2(pi^2)r^2
The integral I solve is \int\int r\phi r\theta...
I had a question regarding how Gauss's law works. I have attached an image that depicts two scenarios.
Basically, if you assume the blue lines are a conductor and the green and red dots both contain an equal amount of charge, what is the expected behavior of the red dot?
As I understand...
According to Gauss's Law, the electric flux through a closed surface is equal to the charge enclosed by the surface divided by epsilon_0. This obviously excludes charges outside the surface. But what about *on* the surface? That is, it lies neither inside nor outside. Does this charge count...
Hi,
I'm just learning about Maxwell's equations in high-school and was playing around with them. Supposedly they are 4 independent and self-sufficient equations that when connected with the Lorentz force law will predict classical electrodynamics in its entirety. But then, it appears to me...
Hi,
I'm seeing that many authors like Griffiths and Halliday/Resnick (I've not seen Jackson and Landau/Lif****z) are deriving the differential form of Gauss's law from the integral form (which is easily proven) by using the divergence theorem to convert both sides to volume integrals and then...
Homework Statement
A very large flat aluminum plate of area A has a total charge Q over its surface. The same charge is placed over the upper surface of a glass plate. Compare the electric fields.
Homework Equations
The Attempt at a Solution
I know how to get the electric field of...
Consider a gaussian surface of arbitrary size and a point charge located outside of the gaussian surface at an arbitrary distance.
Gauss's law states that the flux through the gaussian surface is zero, since there is no charge enclosed by that surface. From this we can deduce that the...
Homework Statement
A uniformly charged ball of radius a and a total charge -Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has a net charge +2Q. Find the magnitude of the electric field in the regions: r_1 < a, a < r_2 < b, b < r_3 < c, and...
I read in Corson and Lorrain that Gauss's law is more gneral than Coulomb's law.It can even be applied to moving charges whatever be their velocities/accelerations.Can anyone explain this?
A long solid nonconducting cylinder or radius R1 is uniformly charged with a charge density (p). It is surrounded by a concentric cylindrical tube or innder radius R2 and outer radius R3, it also has uniform charge density, p. Before I can go on i need to find the electric field as a function of...
I am very confused by this tough question. I hope some experts of Gauss's Law can help me out! Any help is greatly appreciated!
1) A long thin straight wire with linear charge ensity lambda runs down the centre of a thin hollow metal cylinder of radius R. The cylinder has a net linear...
This is a very stupid question. extremely stupid. In fact I'm extremely embarassed.
I was reading a text on electromagnetism, and it said that since the flux due to a charge does not depend on the radius of the sphere then the formula, q/permitivitty applies to all closed surfaces. This is...
if there is not a uniform distribution of charge in the middle how is it possible that there's a uniform field outside. I know why it's true according to gauss's law but it doesn't make sense to me. if there's some positive charge near the interior wall somewhere then there will be an...
i don't understand this. if i have a charge inside a hollow conductor of say +Q and a charge of -Q on the conductor it doesn't matter how close the interior charge is to the wall of the conductor ( but not touching ) the field at all points on the surface of the conductor will be zero? doesn't...
Homework Statement
The Flux of the E-Field is a vector.
It is safer to sit inside a car when lightning strikes than to stand in the open.
If the net charge enclosed by a Gaussian Surface is zero, then by Gauss' Law, the E-Field is zero at all points on the surface.
The Electric flux through a...
A long straight conducting rod (or wire) carries a linear charge density of +2.0uC/m. This rod is totally enclosed within a thin cylindrical shell of radius R, which carries a linear charge density of -2.0uC/m.
A) Construct a Gaussian cylindrical surface between the rod and the shell to derive...
A long straight conducting rod (or wire) carries a linear charge density of +2.0uC/m. This rod is totally enclosed within a thin cylindrical shell of radius R, which carries a linear charge density of -2.0uC/m.
A) Construct a Gaussian cylindrical surface between the rod and the shell to derive...
I have a question about electric flux.
Intuitively it makes that if a charge is outside a closed object, then the net flux inside that object will be zero..but once I write it down on paper it loses its sense.
I attached a picture for clarification.
Flux is equal to the field, times...
I was wondering, how would you prove Gauss's law (either mathematically or intuitively)? I mean, I know that sometimes people take it as the fundamental law (one without proof) but how would you derive such a law from Coulomb's law?
Any help would be extremely appreciated. I have been fussing...