Gauss' law Definition and 334 Threads

"Gauss's theorem can be established as follows. consider an attracting particle of mass m at the point P, and let a cone of small solid angle ω be generated by radii through P. This cone cuts the surface at the points Q1, Q2, ... taken in order from P; the parts of the surface cut off by the...

Homework Statement You have a conducting sphere that is in equilibrium, it has a cavity in it with positive charge +q. If you bring another charge +q2 near the outer edge of the conductor does the total surface charge on the wall of the cavity, q(int) change? There is an image attached that...

Homework Statement A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q. (picture attached) a)What is the total surface charge q(int) on the interior surface of the conductor (i.e., on the wall of...

Homework Statement Two small insulating spheres with radius 9.00×10−2m are separated by a large center-to-center distance of 0.545 m . One sphere is negatively charged, with net charge -2.35 μC , and the other sphere is positively charged, with net charge 4.35 μC . The charge is uniformly...

in a 4D plane or on a four-dimensional surface can gauss law be used?

Homework Statement A long, thin, straight wire of length 1.3 m has a positive charge 4.1 × 10-8 C distributed uniformly along it. The electric field created by this wire at a radial distance 3.2 cm has a magnitude of ε= 8.85E-12 Homework Equations I think I need to use E= q/(4πr^2ε) but I...

Say you have a hollow cylinder, whose one side is open. Now, you pace a positive charge ##Q## at the centre of this open end (such that it is just inside the cylinder). How much should be the flux coming out from the closed end? I just thought of this problem. In order to use Gauss' Law, we...

In the derivation of the electric field inside a non conducting sphere, We still use the permittivity of free space even though we are in a medium. The same applies for ampere's law in a solid wire. http://physics.bu.edu/~duffy/semester2/c15_inside.html...

Hi there. I am trying to derive Gauss's law from the divergence. I would like to know if it is correct: The divergence is defined as (I saw this on Fuller & Byron "Mathematics of classical and quantum physics") ##...

This is probably my misunderstanding, so please clarify. In a region of empty space, there are two point charges with the charges+Q and -Q. Exactly in the middle of the two charges (distance r from both charges) is point P, colinear with the centers of both charges. A Gaussian surface that...

We took today in a lecture gauss' law for magnetism which states that the net magnetic flux though a closed shape is always zero (Monopoles don't exist). The professor explained/proved it as following (Since it needs math theorems): Draw any shape. From the fact that any magnetic field line that...

Homework Statement A point charge q=−5.0×10−12 C is placed at the center of a spherical conducting shell of inner radius 3.5cm and outer radius 4.0 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 8.0 N/C. (a) What is the charge...

Homework Statement Question ==== An infinitely long insulating cylindrical rod with a positive charge ##\lambda## per unit length and of radius ##R_1## is surrounded by a thin conducting cylindrical shell (which is also infinitely long) with a charge per unit length of ##-2\lambda## and radius...

Homework Statement A capacitor has two square plates that are d apart. Each plate is L×L. The capacitor is initially uncharged. (a)Calculate the work required to move q of charge from one plate to the other. (b)Calculate the work required to move an additional q of charge from one plate to the...

the problem: Say we have the entire space uniformly charged. Then, the E field experienced by any point is zero, from symmetry.* But, it means that for any Gaussian surface, the flux though it is zero even though the charge enclosed is clearly not. Gauss' law seems to disagree with symmetry, but...

Suppose the hydrogen atom consists of a positive point charge (+e), located in the center of the atom, which is surrounded by a negative charge (-e), distributed in the space around it. The space distribution of the negative charge changes according to the law p=Ce^(−2r/R), where C is a...

Homework Statement A charged, straight line/rod of infinite length has a Discrete uniform distribution of charge, has a linear density of λ and is at a distance d from a sphere with a radius of R. Find the entirety of the Electrical Flux that is caused by this charged rod, which passes...

Homework Statement An uncharged, unconductive, hollow sphere with a radius R of 10.0 cm, surrounds an electric charge of 10.0 μC, which is found at the beginning of the axises, in a standard cartesian system. Parallel to the z axis, a small drill with a radius r = 1.00 mm opens a hole in the...

Say you had two isolated hydrogen atoms. Because of the spherical distribution of electronic charge on each hydrogen and the net charge of 0 outside each atom, wouldn't Gauss's law dictate a 0 net electric field outside each atom? If this is the case, why does diatomic hydrogen so readily form...

For the proof I've read that verifies transverse electromagnetic waves are consistent with Gauss' Law, there seems to be the suggestion that the magnetic and electric field at a given small length c(dt), along which the waves travel, propagate infinitely backwards and forwards in their...

I noticed the other day something odd in how we use Electric and Magnetic flux. The definitions I refer to are magnetic flux density (B), magnetic flux intensity (H), electric displacement field (D) or Electric field density (D) and electric field (E): B = μH ΦB = B*Area & D = εE ΦE = E*Area...

Homework Statement No variables, just a conceptual question. Homework Equations Flux = EA = Q/ε The Attempt at a Solution Given a uniformly charged rod of FINITE length, could we use Gauss' law for electric flux to calculate the field at a point p a distance x away from the rod, so long as the...

So, this has been bothering me for a few days and I'm having trouble understanding where the fault is. If we consider a uniform charge density ##\rho## extending through all space, then by symmetry, I would argue that ##\mathbf{E}=0## in all space. However, this does not agree with what a naive...

I'm confused as to how this expression E= (δ/εo) can't be used to calculate the electric field of a perfectly flat part of a surface even farther from just above the surface.If you just extend the same cylindrical Gaussian surface used for this proof, wouldn't the field stay the same no matter...

I WAS THINKING ABOUT A REGION OF SPACE WITH ELECTRIC FIELD ALONG POSITIVE X DIRECTION AND Varying WITH SPACE COORDINATE(x) NOW IF ONE IMAGINES A CUBE IN SPACE SUCH THAT FIELD CROSSES ITS TWO FACES AT RIGHT ANGLES ,A SIMPLE Application of...

I've got confused over a topic in my physics textbook (Fundamentals of Physics). The textbook says if a charged particle is enclosed by a shell of uniform charge, there is no electrostatic force on the particle from the shell. I don't firmly get this, as the book uses a confusing reasoning for...

Homework Statement An infinite metal plate has a surface density of charge σL=-6μC/m² , Left side and a surface density Of load σR=+4μC/m² , in the right side. A Gaussian surface In the form of a circular cylinder, with area A 12 cm², is Located with the left side inside the plaque and a thin...

According to Gauss Law, we only consider charges which are inside the surface to produce net flux. We disregard the charges outside the surface because they produce zero net flux (as the electric field lines enter the surface and leave the surface producing zero net flux) My question is, since...

Homework Statement A metallic sphere of radius a is placed concentrically with a metallic spherical shell with inner radius b and outer radius c. The sphere has a total charge of 2Q and the shell has a total charge of 3Q. (a) What is the charge distribution? Specifically, what is...

Homework Statement I keep getting confused about this part of Gauss' law. Is the da on the left side the surface area of the the Gaussian surface? and on the right side when I am integrating. I say that q = the charge density multiplied by something. Is that something surface area of the...

Homework Statement An isolated conductor has a net charge of +14.0 × 10- 6 C and a cavity with a particle of charge q = +4.30 × 10-6 C. What is the charge (a) on the cavity wall and (b) on the outer surface? Homework EquationsThe Attempt at a Solution So I understand that B is just adding the...

Knowing that Gauss' law states that the closed integral of e * dA = q(enclosed)/e naut, how would you find exactly what A is in any given problem? I know it varies from situation to situation depending on the geometry of the charge. For instance, I know that for an infinite wire/line of...

I'm confused with the electric field inside a sphere. The book said that E=keQr/a^3 While one of the properities of electrostatic equilibrium mentioned that the E-field is zero everywhere inside the conductor. Are there any exceptional cases? Thanks in advance.

Firstly I appologize, that I am not native english speaker and I don't study physics(but cybernetics we are getting just some general knowledge about physics), but hopeffuly I will write this right. Homework Statement We know that inside of a conductive object is protected from influence of...

Hi. Is it possible to derive the properties of a Faraday cage from Gauss' law alone? I found some "derivations" which I find rather unconvincing since they somehow conclude from a vanishing flux that the E field must vanish as well. Some slightly more elaborate derivations use a combination of...

Hi. Is the Maxwell equation $$\nabla\cdot\vec{E}=\frac{\rho}{\varepsilon_0}$$ even true in the stronger form $$\frac{\partial E_i}{\partial x_i}=\frac{\rho}{3\cdot\varepsilon_0}\enspace ?$$ I guess not, since I haven't found a source suggesting this. But shouldn't the isotropic electric field...

Lets consider a hollow sphere with charge +q and than a larger hollow sphere that encloses it with -q, so two spheres one inside the other. Now we use draw an even larger Gaussian sphere that encloses both of these, ∫EdA = Qinclosed/ ∈_0 the total enclosed charge is +q + -q = 0 so ∫EdA = 0 E...

I was looking for a derivation of E=(2kλ)/r for an infinite line of charge. I understood that you need to use Gauss's Law and a cylinder around the line. When looked it up, I found this: http://www.vizitsolutions.com/portfolio/gausslaw/lineCharge.html He starts out with ∫E⋅dA=4πq. I have never...

Homework Statement I need help in figuring out if I have done this problem correctly. From what I understand ∫E * dA = E*A, where E is the electric field and A is the area of a side. My biggest concern is if I can plug in the length "L" for the "x" and "z" variables within "E = -5x * E0/L i +...

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...

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 Hello, A 3.60cm x 4.50cm rectangle lies in the xy-plane. What is the electric flux through the rectangle if E=(80.0i + 50k) N/C ?Homework Equations Φ = E * A =EAcos(θ) The Attempt at a Solution My attempt: First convert the rectangle units from cm to m. 4.50cm = 0.045m...

Hello, The problem: A 3.60cm x 4.50cm rectangle lies in the xy-plane. What is the electric flux through the rectangle if E=(80.0i + 50k) N/C ? My attempt: First convert the rectangle units from cm to m. 4.50cm = 0.045m 3.60cm = 0.036m Find the area of the rectangle. A = 0.036m x 0.045m =...

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...

Why does Gauss' law hold for any closed surface? and can you show this mathematically. Many thanks :)

Homework Statement Hi, I am studying gauss's law via this book below.[/B] http://faculty.polytechnic.org/cfletcher/Phys%20With%20Calc_Vol_2_web_pdfs_2010/i-Ch14-PCALC--GAUSS'S%20LAW.pdf On page 8, and 9, the book describes the shell method of finding the volume of the sphere and then using...

Homework Statement The volume between two infinite plates located at x=L and x=-L respectively is filled with a uniform charge density ##\rho##. Calculate the electric field in the regions above, between and below the plates. Calculate the potential difference between the points x=-L and x=L...

Homework Statement I have attached the problem Homework Equations E*A = Qenc/ E0 The Attempt at a Solution At the moment I am looking at the problem more conceptually and seeing what is happening at each point and I wanted to know If I was on the right track. r<a As all charge would...

Homework Statement Three concentric hollow spherical conductors are charged as follows: the inner conductor carries charge Q, the middle conductor carries charge -2Q, and the outer conductor carries charge -Q. What is the charge on the outer surface of the middle conductor? Homework Equations...

Homework Statement We have a wire of the length L=0.2m which is uniformly charged with a linear density of Lambda = 3nC/cm. Find the intensity (E) of the electric field in point A1 whose perpendicular distance from the wire is a=0.05m. The wire is in a vacuum. Compare the intensity with the...