Gauss's law Definition and 384 Threads

Can we use Gauss's Law to calculate the field distribution around an electric dipole?

Homework Statement There are two conducting spheres, one hollow outer sphere which originally had +60nC of charge on it, and a smaller inner sphere enclosed by the hollow outer sphere which contains +20nC of charge. Homework Equations INT(E.DA) = Qenclosed/epsilon0 The Attempt at a...

Homework Statement Calculate the flux through the surface of a disk-shaped area of radius R = 5.00 cm that is positioned perpendicular to and centered on the axis of the solenoid as shown below The Attempt at a Solution \oint \vec{B} \cdot \vec{dA} = \Phi_{B} \vec{B} =...

Homework Statement A spherical cavity of radius 4.50 cm is at the center of a metal sphere of radius 18.0 cm. A point charge Q = 6.40 µC rests at the very center of the cavity, whereas the metal conductor carries no net charge. Determine the electric field at the following points. (a) 2.0...

Homework Statement Calculate the gravitational potential due to a thin rod of length l and mass M at a distance R from the center of the rod and in a direction perp. to the rod. Homework Equations integral form of Gauss's law wrt gravitation The Attempt at a Solution Can I use...

Homework Statement An initially neutral conductor contains a hollow cavity in which there is a +100nC point charge. A charged rod transfers -50nC to the conductor. Afterward, what is the charge (a) on the inner wall of the cavity wall, and (b) on the exterior surface of the conductor...

Homework Statement My book says Now here is the thing I have two situations (1) Consider a hollow conducting sphere with a net charge +Q and a conducting solid sphere with a net charge -Q. The solid one is inside the hollow conducting sphere. If I were to construct a Gaussian...

A solid sphere of radius R has a non-uniform volume charge density \rho(r) and a constant surface charge density \sigma. If the field inside the sphere is uniform and radially atuned, and the field a distance 2R away from the center is zero, find \rho and \sigma in terms of R, r (distance from...

I know what formula you need to solve this problem (the attachment), but I'm having trouble with understanding the signs and direction of points A,B, and C. I know that the lines go towards the negative and away from the positive, but I'm still not seeing the correct signs. For instance I...

Homework Statement A 8.0 charge and a -4.9 charge are inside an uncharged sphere. What is the electric flux through the sphere? Homework Equations It says in the book that Electric flux = E(4piR^2) although I do not know the radius and yet still don't believe that's the way to go to...

Homework Statement A closed surface with dimensions a = b = 0.400 m and c = 0.800 m is located as shown in the figure below. The left edge of the closed surface is located at position x = a. The electric field throughout the region is nonuniform and given by E = (2.70 + 2.20 x2)i N/C, where x...

Homework Statement A particle with charge Q is located immediately above the center of the flat face of a hemisphere of radius R as shown in the figure below. https://www.webassign.net/serpop/p19-33.gif (a) What is the electric flux through the curved surface? (Use any variable or...

Homework Statement Determine the magnitude of the electric field at the surface of a lead-199 nucleus, which contains 82 protons and 117 neutrons. Assume the lead nucleus has a volume 199 times that of one proton and consider a proton to be a sphere of radius 1.20 10-15 m. Homework...

I am taking a course in Electromagnetic Wave Theory, and the prescribed book for us is Engineering Electromagnetics by William Hayt. The book if excellent, till I reached the part about Gauss's Law. I will be describing my queries here, kindly help me out with them. 1) The book first states...

Hi I have some questions about the Gauss's law for electric field. Wikipedia definition says Now how did Mr Gauss arrive at this conclusion regarding any closed surface ? That is a very general statement. And during his time, were there instruments which could have lead to the formulation of...

Gauss's Law - A hollow sphere with inner and outer radius! Homework Statement A spherical shell of inner radius R1 and outer R2 carries a charge Q that is uniformly distributed throughout its volume. No other charges present. a)calculate E inside the sphere b)within the volume c)outside...

Homework Statement a)A charge Q=10nC is placed at the origin, which is the centre of a cube with side lengths a=1cm whose faces are perpendicular to the x,y and z axis. What is the total flux through the box and what is the average of the perpendicular component of the electric field on the...

Homework Statement Find the net electric flux through the spherical closed surface shown in the figure below. The two charges on the right are inside the spherical surface. (Take q1 = +1.96 nC, q2 = +1.03 nC, and q3 = -3.09 nC.) https://www.webassign.net/serpse8/24-p-006-alt.gif The...

Homework Statement A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of lambda, and the cylinder has a net charge per unit length of 2lambda. From this information, use Gauss's law to find (a) the...

Can someone please help me work through this problem I've spent over an hour on this trying to figure out what to do.. here's the question A nonuniform electric field is given by the expression E = ay^i + bz^j + cx^k, where a, b, and c are constants. Determine the electric flux through a...

Homework Statement A long straight metal rod has a radius of 5.00cm and a charge per unit length of 30.0nC/m. Find the electric field a) 3.00cmThe Attempt at a Solution It says a) = 0 I did some math and I got 2k\frac{\lambda}{r} The rod is solid, so should a E-field be radially outward...

Homework Statement Homework Equations {\phi} = \int E dA = \frac{QL}{\epsilon_0} The Attempt at a Solution I'm aware of the definition of Gauss's law of electrostatics (however evidently I'm not very good at applying it), but I can't seem to fully answer the rest of the question...

Homework Statement 1) A point charge is placed at the centre of a spherical Gaussian surface. Is ΦE changed, a) if the surface is replaced by a cube of the same volume? b) if the charge is moved off centre in the original sphere, still remaining inside? 2) A point charge q is placed at the...

Homework Statement (first of all, let me know if I am wrong in any parts) gauss's law can be used on cylinder. Why is it that flux on top and flux on bottom of the cylinder, with area pi*r^2 ignored? (aka, equal to 0) such that Flux= Integral(E*da)=E2(pi)rl=q/(Eo) where (Eo) is permitivity...

I was searching the forums and I found someone asking the same question a while back, but i am totally confused, I thought I was understanding this stuff up to this point. http://answers.yahoo.com/question/index?qid=20100928212107AAwXTlT&r=w I posted and wrote up the whole problem on...

QUESTIONS 5.The electric field E is zero at all points on a closed surface; is there necessarily no net charge within the surface? If a surface encloses zero net charge, is the electric field necessarily zero at all points on the surface? 6.Define gravitational flux in analogy to electric...

Negative charge - Q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin. Find the x-component of the net electric field at the origin. Find the y-component of the net electric field at the origin.

There are basically three types of charge densities; linear \lambda (over a thin ring or rod), surface \sigma over a thin flat surface, and over a volume \rho The problem is how these densities produce an electric field: applying Coulomb's law for the electrostatic force using appropriate...

We know that the Gauss's law expressed in the differential form is: \mathbf{\nabla}\cdot\mathbf{E} = \frac{\rho}{\epsilon_0}, right? I read at wikipedia that \rho is: the total charge density including dipole charges bound in a material. I don't understand... The left side of...

So I'm reading Div, Grad, Curl and All That which is my only exposure to Maxwell's equations. The author started with the integral form of Gauss's law (which I get), where the surface integral of the electric field = the enclosed charge (q) divided by epsilon nought. But in deriving the...

What is the difference between coulomb's law and gauss's law ? because both are giving same results while calculating electric fields ? what is the basic difference. are they same?

Homework Statement A long thin wire, hundreds of meters long, carries a uniformly distributed charge of -7.2 microCoulombs per meter of length. Estimate the magnitude and direction of the electric field at points (a) 5.0 m and (b) 1.5m perpendicular from the center of the wire. Homework...

I have difficulty when trying to decide which form of Gauss's law I should use for a problem. Please, tell me when I should use the integral form: \int E \cdot dA = \frac{Q_{in}}{\epsilon_{0}} and when it's appropriate to use the other form: E \cdot A = \frac{Q_{in}}{\epsilon_{0}}

1. Homework Statement A long, thin straight wire with linear charge density \lambda runs down the center of a thin, hollow metal cylinder of radius R. The cylinder has a net linear charge density 2(\lambda). Assume \lambda is positive. Find expressions for the magnitude of the electric...

Gauss's Law and Superposition of Fields (edited again, something else wrong) Homework Statement Right. The shape itself has charge Q, so it has charge density \frac{Q}{\frac{4}{3} \pi R^3 - \frac{4}{3} \pi (\frac{R}{2})^3} = \frac{6Q}{7\pi R^3} Let's call this \rho. If it were filled in...

Homework Statement The box-like Gaussian surface of the attached figure encloses a net charge of +24.0 \epsilon_0 \mu C and lies in an electric field given by \vec E = [(10.0 + 2.00x) \hat i - 2.00 \hat j + bz\hat k]N/C with x and z in meters and b a constant. The bottom face is in...

Homework Statement A thin metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the shell and another charge q1 is placed outside it. All the three charges are positive. Find (a) the direction of the force on the charge at the centre, and (b) the...

When should I use one and when should I use the other? For example, suppose I have a rod of length 2L, with an edge on the point -L on the X axis and another on L. The rod is uniformly charged, with total charge Q>0. having that said, if i wanted to calculate the electric field in an arbitrary...

Homework Statement A sphere of radius R has a total charge +Q, uniformly distributed throughout its volume. It is surrounded by a thick spherical shell of inner radius R and outer radius 2R carrying a total charge -Q, also uniformly distributed throughout its volume. Using Gauss's law...

There are two spherical hollow conducting shells, one inside the other. The outer shell has a radius 4 times that of the inner shell. There is a switch connecting the two shells, which is for the moment, open. Both shells have a positive charge (inner shell = +20nC and outer shell = +60nC...

so my book has a point charge q inside an arbitrary surface S and at a point P on the surface S, the electric field is E = q/4(π)(ε0)(r2). so the flux through S is then dΦ = E * dS = q/4(π)(ε0)(r2) * dS = q/4(π)(ε0) * dScosθ /(r2) = q/4(π)(ε0) * dΩ. then my book takes the integral of both sides...

Homework Statement A spherical shell of radius 4 m is placed in a uniform electric field with magnitude 7020 N/C. Determine the total electric flux through the shell. Answer in units of N · m^2/C. Homework Equations Gauss's Law The Attempt at a Solution I thought this would be as simple as...

[b]1. Two long charged, concentric cylinders have radii of 3.0 and 6.0 cm. The charge per unit length is 5.0 x 10-6 C/m on the inner cylinder and -7.0 x 10-6 on the outer cylinder. Find the electric field at (a) r = 3.0 cm and (b) r = 8.0 cm, where r is the radial distance from the common...

In electrostatic case, Gauss's law can be derived from Columb's law, so we can regard experimental evidence for Columb's law as evidence of Gauss's law. But what about non-static case? In this case we know columb's law is no longer valid, so we need experimental evidence to justify Gauss's law...

http://img404.imageshack.us/img404/4148/gauss3j.png (infinitly long) \Phi=\Phi_{0}(1-{r \over R}) {C \over m^2} What's the charge of the cylinder of length L? Again, almost everything was wrong...

Homework Statement A charge of 9 pC is uniformly distributed throughout the volume between concentric spherical surfaces having radii of 1.8 cm and 3.8 cm. Let: Ke = 8.98755 × 109 N · m2/C2 . What is the magnitude of...

As you probably know, there is a formal proof of Gauss's Law for electric fields based on Coulomb's Law and the concept of solid angles. How can one prove Gauss's Law for magnetic fields? Is there a similar proof based on solid angles?

Homework Statement There are four charges, each with a magnitude of 3.04C. Two are positive and two are negative. The charges are fixed to the corners of a 0.124-m square, one to a corner, in such a way that the net force on any charge is directed toward the center of the square. Find the...

http://www.twiddla.com/188165 R and Q are given E(P)=? phi(P)=? The Attempt at a Solution Homework Statement Homework Equations I have no idea. I managed to do phi=E*2pi*r*h

Homework Statement An atom that has Z protons, each with positive charge of magnitude e, reside in the nucleus at the center, surrounded by a uniformly distributed spherical cloud of radius R consisting of Z electrons, each with negative charge magnitude e, centered on the nucleus e. Use...