Gauss' law Definition and 341 Threads

Homework Statement The figure shows cross-sections through two large, parallel, nonconducting sheets with identical distributions of positive charge with surface charge density σ = 1.06 × 10-22 C/m2. What is the y component of the electric field at points (a) above the sheets, (b) between them...

I am stuck with this (d) all the other (a),(b),(c) were just like (a) E= −∇φ (b) ∇ · E= −∇2φ (c) ∇ × E I know only very basic about Gauss' law, the problem is not from Electrodynamics course. I don't know what should I do to solve (d)

1. Homework Statement I need to find the total charge inside the small metal sphere, inside the big metal sphere as well as outside the big metal sphere. Homework Equations What confuses me is the electric field vector. Since it's only poiting in one direction it can't originate from a...

Homework Statement Consider two balls of equal radii and masses but opposite charges, distributed uniformly over their volumes. Initially, the balls are at rest and far away from one another. Due to the Coulomb attraction, the balls start moving towards each other. The balls can be treated as...

Homework Statement Homework Equations Gauss' Law: ∫E⋅da = qenc/ε0 E-field: E = kq/r2 The Attempt at a Solution I solved this using electric field equation, differential elements, and integration. The correct answer is, I think, E=-q/(8πε0R2) QUESTION: Can this be done via Gauss' Law? The...

Homework Statement [/B] Assume that the infinite wall −2 < y < 2 is filled with a uniform charge of density ρv = 3 C/m3. Obtain an expression for Ey at a general point (0,y,0) and plot Ey as a function of y over −5 < y < 5. Homework Equations E = ρv / ( 4 π ε0 ρ) ∫∫∫D⋅ds = Qenc The Attempt at...

In my physics textbook, I see Gauss' Law as https://upload.wikimedia.org/math/0/3/5/035b153014908c0431f00b5ddb60c999.png\ointE dA but in other places I see it as...

Homework Statement (a) A spherical insulating shell of radius R = 3.00 m has its centre at the origin and carries a surface charge density σ = 3.00 nC/m2. Use Gauss’s law to find the electric field on the x-axis at (i) x = 2.00m and (ii) x = 4.00 m. Give you answers in the vector form. (b) A...

I've been given a copy of my friend's midterm exam from this same class from last term, and decided to take a crack at it to help study. One question type in particular really messes me up and it looks like the following. How would I go about solving these in the future? A solid insulating...

Homework Statement A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x=d and x=−d. The y- and z-dimensions of the slab are very large compared to d and may be treated as essentially infinite. Let the charge...

Gauss law in case of sphere which has charge ##q## is ##\oint \vec{E}\cdot d\vec{S}=\frac{q}{\epsilon_0}## Is there some anologone for case of sphere with mass ##m## such that ##\oint \vec{G}\cdot d\vec{S}=4\pi \gamma m ## and what is ##\vec{G}## in that case?

Homework Statement A closed rectangular surface with dimensions a = b and c where the faces perpendicular to the field are a*b. The left edge of the closed surface is located at position x = a, for c > a.The electric field throughout the region is nonuniform and given by E = 3*x xhat N/C...

Homework Statement A coaxial cable consists of two concentric cylindrical conductors as shown here: http://puu.sh/luFZx/7f3e1ccb07.png . The inner cylinder has a linear charge density of +λ1, meaning that each meter of the cable will have λ C of charge on the inner cylinder. The outer cylinder...

Homework Statement A spherical capacitor consists of two concentric spherical conductors of radii ##R_{1}## and ##R_2, (R_2 > R_1)##. The space between the two conductors is filled with a linear inhomogeneous dielectric whose relative permittivity varies with the distance ##r## from the...

Homework Statement An infinite plane of charge has surface charge density 6.8 µC/m2. How far apart are the equipotential surfaces whose potentials differ by 100 V? In mm Homework Equations E=σ/(2ε0) The Attempt at a Solution So first I solved for E= 6.8e-6/(2*8.85e-12) = 384170.791 then...

Homework Statement A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has total charge -2q and the outer shell has charge +4q. a) calculate the electric field...

I'm trying to understand how the integral form is derived from the differential form of Gauss' law. I have several issues: 1) The law states that ## \nabla\cdot E=\frac{1}{\epsilon 0}\rho##, but when I calculate it directly I get that ## \nabla\cdot E=0## (at least for ## r\neq0##). 2) Now ##...

Homework Statement A cylindrical shell of radius R and length H has its charge uniformly distributed on its curved surface Find the electric field at a point P from the axis, a distance r away, measured radially outward from the midpoint of the shell such that R>r Homework Equations φ =...

Homework Statement The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. Assume that these protons are incident on the Earth’s atmosphere from all directions at a rate of 1366. protons per square meter per second. Assuming that the depth of Earth’s atmosphere...

I'm currently writing my EP on various physical equations including Maxwell's equations, and I had to justify using the dot product of the normal unit vector and the electric field in the integral version. However, I can't think of a reason for not using trigonometry as opposed to the...

How did Gauss came out with his law εΦ=Qenc,where Φ is the flux and Qenc is the net charge inside the gaussian surface?Was it an experimental work or just a theoretical one? thanks.

I’ve been searching for a proof, using the equation for the electric field due to a moving point charge – given, for example, on page 438 of the Third Edition of David Griffith’s Introduction to Electrodynamics (equation 10.65) – that Gauss’s law holds for a moving point charge. There is no such...

Homework Statement If a point charge is inside a Gaussian sphere but is off center, why is its electric field still Qenc/(e0*4*pi*r^2)?Homework Equations surface integral of E*da=Qenc/e0The Attempt at a Solution If we draw cones out from the charge. the 2 surfaces from the cones' intersection...

Homework Statement Assume that a ball of charged particles has a uniformly distributed negative charge density except for a narrow radial tunnel through its center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton anywhere along the...

Flux through a closed surface is zero due to external charge but why it is not so in case of sphere

At the exact center of a finite wire (i.e. a distance, say $L/2$ from each end), why can I not apply Gauss's Law in integral form to find an EXACT solution for the electric field? At the center of the wire, $E$ is entirely radial, so it seems like I should be able to draw an infinitesimally...

If F(x,y,z) is continuous and for all (x,y,z), show that R3 dot F dV = 0 I have been working on this problem all day, and I'm honestly not sure how to proceed. The hint given on this problem is, "Take Br to be a ball of radius r centered at the origin, apply divergence theorem, and let the...

I recently studied Gauss' theorum according to which there is no electric field inside a closed conductor. But an isolated chage emits field lines in all possible directions. So why is it that there are no electric lines from the surface of the closed conductor inside it?

Homework Statement I've been doing a few Gauss' Law problems and I'm slightly confused about calculating charge enclosed by a nonconducting sphere. So I have done 2 problems that involve finding the electric field inside nonconducting spheres: 1. Charge is uniformly distributed 2. Charge per...

Homework Statement According to an old model due to JJ Thompson, an atom consists of a cloud of positive charge within which electrons sit like plums in a pudding. THe electrons are supposed to emit light when they vibrate about their equilibrium positions in this cloud. Assume that in the case...

Homework Statement Two large, flat metal plates are separated by a distance that is very small compared to their height and width. The conductors are given equal but opposite uniform surface charge densities +- \sigma. Ignore edge effects and use Gauss's law to show a) that for points far...

Homework Statement Figure 23.52 gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by Es = 5.0 x 10e7 N/C. What is the charge on the sphere? Homework Equations Net Flux...

Homework Statement A solid insulating sphere of radius 5.0 cm shown in blue has a uniform charge density throughout its volume. Concentric with this sphere is a conducting thick hollow spherical shell of inner radius 20.0 cm and outer radius 25.0 cm shown in grey. The electric field at a point...

Ok, so a lot people said that 1. the charge outside of the enclosed surface wouldn't influence the total flux that penetrate the surface 2. q/ε wouldn't change if the charge inside the surface does not change (see my painting, so it can help you understand what i meant) i was ok with these...

This is my first time using a website like this, so I sincerely apologize if I'm posting in the wrong spot, I'm just in a bind/frustrated with this seemingly easy problem. Homework Statement What is the electric potential at a point 0.80 m away from a point charge of 3.5m C? Homework...

When I learned Integrals in Calc III, the formula looked like this ∫∫ F(r(s,t))⋅(rs x rt)*dA but in physics for Gauss's law it is ∫∫E⋅nhat dA How are these the same basic formula? I know that nhat is a unit vector, so it is n/|n|, but in the actual equation, it is a dot between the cross...

Hello everyone. I've been asked the following question by someone and I'm not quite sure which is the correct answer. I'd appreciate some help with it. The question is pretty simple: When can't be Gauss's law applied? 1. When the electric field of a point charge is dependent on the angles...

Homework Statement A charge distribution is given by ##\rho(r,\theta,phi)=\gamma r^3cos\theta,a<r,b,0\leq\theta\leq\pi/2## and is zero everywhere else. The distance from the origin ##r=\sqrt{x^2+y^2+z^2}## and ##\gamma## is a constant. Write out the electric field P along the z-axis a distance...

A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x=d and x=−d. The y- and z-dimensions of the slab are very large compared to d and may be treated as essentially infinite. The slab has a uniform positive charge...

This is what we have in text-books and in Wikipedia: ρ=ρb+ρf and from there we get ∇.D=ρf. But I am unable to understand why we are not considering the bound surface charge in deriving this equation. Can anyone explain this to me.

I know how to derive Gauss's law considering only one point charge and a sphere. I've seen other derivations for other geometrical shapes and I would say this is way too tedious as a method to prove that Gauss's law always holds true. I was wondering if there is a general proof that says...

Hi everyone, I am struggling with gauss law. I understand the basic concept , but I can not relate it to other physics problems. I have this physics problem. I want to really understand physics, but I can't. I have watched a lo of videos but I still don't understand. I am going to give my...

Homework Statement Problem statement: An infinitely long, straight line has a uniform charge distribution of ρ C/m. Use Gauss' law to find the electric field at a point r m away from it. Solution: Consider a cylindrical volume of height ℓ with circular cross sectional area of radius r...

I'm stuck on some high school physics, Gauss law... 1. It says this: The electric field outside the sphere is equal as if the charge of the sphere was in it's center. I don't understand this, why is this true? I get it - experiments have showed that and that's how you calculate it; but what's...

Homework Statement Q) Use Coulomb’s Law to DERIVE the Gauss Law result for the particular case of A SINGLE POINT CHARGE. That is, using Coulomb’s Law, find the ELECTRIC FLUX going through a sphere of radius r surrounding one point charge of charge-magnitude q. THANK YOU Homework...

For an infinite plane sheet of charge it is obvious that the E-field points directly perpendicular to the sheet. but for conductors of irregular shape. say, a wire, or even a sheet with imperfections in it, what guarantees that the E-field will point directly perpendicular from the emanating...

Homework Statement A Gaussian Sphere with a radius of 1m surrounds an unknown charge at the center. At this surface a uniform outward directed electric field is 1 N/C. Use Gauss' Law to calculate the amount of charge enclosed by the sphere. Homework Equations E = q/4∏εor^2 The Attempt at a...

Homework Statement The charge density of a spherically symmetric and uniform distribution of charge is ρ = 2*10^-3 C/m^3. An electron is released one centimeter from the center. Find the magnitude and direction of the force onto the electron.Homework Equations charge density = Q/V =...

Hello, i'm doing some practice problems using Gauss' law, but I feel like my work is 'sloppy'. I'll show an example, where I think I get the right answer, but it feels like I'm neglecting to treat the summation properly, or perhaps I don;t quite understand why what I'm doing is fine...

Suppose that you have a region of space with no fields and the only matter is in the form of a cloud of point-masses. On the one hand, within the cloud, the stress-energy tensor vanishes almost everywhere (except right at the point-mass, in which case it is infinite). So the Einstein tensor...