A law in Classical Electromagnetism and Newtonian Gravity.

learn more… | top users | synonyms

-3
votes
0answers
42 views

Gauss Law - Variable Electric Field Perpendicular to Sheet [on hold]

So imagine a square sheet parallel to the x-y plane that has a perpendicular electric field (in the z direction) flowing through it such that $$E=\gamma x$$ where $\gamma$ is a constant value (lets ...
2
votes
2answers
69 views

Gauss' law question

It's actually a teaching conflict at my school. They said that $$\text{Flux}=\frac{q}{\varepsilon_0}.$$ Say for a point charge at the centre of the sphere and let's say we not put water into the ...
0
votes
0answers
23 views

Law of Gauss. Electrostatics

I have seen on the internet that many times people assert that inside a cylindric condenser the electrostatic field is null due to the fact that the Gauss flux inside is null. But I wanted to make ...
1
vote
1answer
42 views

What is the electric field between and outside infinite parallel plates?

I know that Gauss's law says $$\oint_S {\vec{E} \cdot d\vec{A} = \frac{q_{enc}}{{\epsilon _0 }}}$$ and that because $\vec{E}$ is always parallel to $d\vec{A}$ in this case, and $\vec{E}$ is a ...
2
votes
2answers
127 views

2D Gauss law vs residue theorem

I used to have a vague feeling that the residue theorem is a close analogy to 2D electrostatics in which the residues themselves play a role of point charges. However, the equations don't seem to add ...
1
vote
1answer
88 views

Why does Gauss's law work for a charge off center in a spherical surface?

CASE 1: Consider an enclosed spherical surface with a charge $q$ at its centre. From Gauss' law we can say that the flux through this sphere is $q/\epsilon_0$. CASE 2: The charge is inside but off ...
4
votes
3answers
131 views

Integral form of Gauss's law for magnetism from Stokes' theorem?

How can the integral form of Gauss's law for magnetism be described as a version of general Stokes' theorem? How does it follow?
1
vote
2answers
34 views

Gauss' Law for Magnetism Derivative Form: With or without volume integral?

I've been reading through FLP Vol. II, and he has proven that as the flux through a closed surface is: $\ \int_{surface} \mathbf{F} \space \mathrm{d}\mathbf{a} $, according to the divergence theorem, ...
3
votes
1answer
52 views

Can Gauss' Law in differential form apply to surface charges?

I'm calculating the electric field outside a coaxial cable using only Gauss' Law in differential form. The charge density on the interior solid conducting cylinder is exactly cancelled by the surface ...
0
votes
1answer
73 views

Am I interpreting Gauss' Divergence Theorem correctly

I was reading Introduction to Electrodynamics by Griffiths and I wanted to check if I understood Gauss' Divergence Theorem correctly. The theorem states: $$\int \int \int_V \vec{\nabla} \cdot \vec{C} ...
0
votes
0answers
15 views

Electric field for two adjacent infinite layers of width h charged + and − uniformly

I'm trying to figure how to calculate the electric field created by two adjacent infinite layers of width h charged + and − uniformly. I don't understand why isn't the field outside of the layers ...
1
vote
0answers
39 views

Gauss's Law problem [closed]

I've been thinking about this for a while, but I'm not sure how to proceed. I understand uniform charge-density problems, but the added non-uniform deal makes me uneasy: find the e. field inside a ...
1
vote
0answers
19 views

Electric Field: distributed uniformly in one infinity tape of length [closed]

One charge density surface is distributed uniformly in one infinity tape of length with $2a$ width from distance $d$. Determine the Electric Field in the point perpendicular from the distance $d$ ...
2
votes
0answers
33 views

Electric field of a capacitor in dielectric medium with weird size

I have been learning gauss's law in capacitor recently, recently I come up with this problem that I couldn't solve myself. If we have a capacitor,and a dielectric medium with half the volume between ...
1
vote
1answer
42 views

Electric field in a cylinder

We have electric charge density $\rho(r) = kr$ in a cylinder of infinite height and radius $a$. I'm asked to find the electric field. I'm doing it using two methods and I don't undesrtand why then ...
0
votes
2answers
68 views

What is meant by “net charge”?

Lets consider a system of two opposite charges separated by a certain distance (dipole), if we ask what is the net charge for this system? the answer would be zero. The net charge (what I have come ...
1
vote
0answers
37 views

How to prove Gauss's law div(E) = rho/epsilon from Coulomb's law? [duplicate]

As we know from coulomb's law that: $$\vec{E} = \frac{q}{4\pi\epsilon R^2} \hat{R}$$ using the above equation, how can I verify that: $$\vec{\nabla}\cdot \vec{E}=\frac{q}{\epsilon}$$ I have tried to ...
2
votes
1answer
229 views

Finding electric field between overlapping surfaces [closed]

The problem is: A sphere with radius R is centered at the origin, an infinite cylinder with radius R has its axis along the z axis, and an infinite slab with thickness 2R lies between the planes ...
5
votes
3answers
414 views

What is the purpose of differential form of Gauss Law?

I am learning the differential form of Gauss Law derived from the divergence theorem. $${\rm div}~ \vec{E} =\frac{\rho}{\epsilon_0}.$$ So far in my study of math and physics, the word "differential" ...
0
votes
0answers
124 views

Apply Gauss' Law to find Electric Field around nonconducting plastic sheets

The question: Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities $\sigma_1$,$\sigma_2$,$\sigma_3$ and $\sigma_4$ on their surfaces, as shown in the ...
0
votes
0answers
28 views

Gauss law from Gauss divergence theorem [duplicate]

Apply Gauss divergence theorem to the gravitational field due to a spherical object of mass M and uniform density located at origin. Obtain Gauss law for gravitation in integral and differential ...
1
vote
1answer
129 views

Maxwells' equations and Coulomb's law

Coulomb's law and Maxwell's equations should be consistant as one can be derived from the other. Say we have a point charge with such a charge that $-kq=1$, meaning that at any point the electric ...
1
vote
1answer
284 views

How to choose Gaussian surfaces while solving problems?

I have a doubt regarding this problem: Two large identical flat metal plates are placed parallel to one another, seperated by a small distance compared to their linear size. One plate is given a ...
1
vote
1answer
81 views

Flux through a conduting cylinder?

A point charge of magnitude $Q$ is placed inside a conducting cylinder of length $L$ and radius $R$ at its centre. What is the flux through the cylinder? I know that I have to use Gauss Law here ...
1
vote
1answer
98 views

Why Gauss' law is applied?

Why Gauss' law is applied? Why is there a need of finding electric field by Gauss' law if we can find the electric field through Coulomb's law? or has it got more applications than Coulomb's law?
0
votes
2answers
102 views

Electric flux due to external charge

Why is electric flux due to external charge i.e a charge outside a closed surface equal to 0? P.S:Moreover I found this statement confusing:- Electric field appearing in the Gauss' law is the ...
0
votes
0answers
26 views

Proof of Gauss' Law [duplicate]

How would you prove Gauss' law for an asymmetrical closed surface? I can find it for symmetrical surface but couldn't for Asymmetrical surfaces.
1
vote
0answers
41 views

Do these steps demonstrate that acceleration of charged particle is proportional to current?

One formulation of Maxwell's Gauss Law for electric field is: $$\bigtriangledown E = 4 \pi k \rho $$ This can be worked into the Divergence Theorem as follows: $$\int\int_{A} F_\perp \:dA= 4\pi k ...
3
votes
2answers
120 views

Relation between Gauss' law and Coulomb's law

In Coulomb's law if the relation was as if electric field intensity was to vary inversely $1/r$ with distance rather than the inverse $1/r^2$ of square of distance, would the Gauss's law still be ...
5
votes
2answers
205 views

Is there a good experiment to demonstrate Gauss's Law for Magnetism?

I'm trying to come up with a simple experiment that can demonstrate the properties of Gauss's Law for Magnetism. I am aware that it is a mathematical representation of the fact that magnetic ...
1
vote
3answers
185 views

Electric flux for a rectangular surface? [closed]

I have the following homework problem: A line of charge $\lambda$ is located on the z-axis. Determine the electric flux for a rectangular surface with corners at coordinates: $(0, R, 0)$, ...
1
vote
2answers
2k views

If we change the radius of spherical surface does electric field or flux change?

Suppose a point charge is located at the center of a spherical surface. The electric field at the surface of the sphere and the total flux through the sphere are determined. 1).What happens ...
-2
votes
1answer
141 views

Why is electric flux through any closed surface $q/\epsilon_0$?

Why is electric flux through any closed surface $q/\epsilon_0$? In schools we are only taught of its simplest case, i.e. flux through a sphere with charge centered at origin. And then it is ...
3
votes
1answer
503 views

Electric Field from Dielectric Shell

This is a question taken from a past E&M exam A thick spherical shell (inner radius $R_1$ and outer radius $R_2$) is made of a dielectric material with a "frozen in" polarization ...
1
vote
3answers
582 views

2 dimensional Coulomb's law equation

We can notice that in the Coulomb's law equation, $$\begin{equation}\tag{1}F=\frac{1}{4\pi\epsilon}\cdot\frac{q_1q_2}{r^2}\end{equation} $$ $4\pi r^2$ factor in the denominator expresses directly ...
2
votes
2answers
173 views

My conundrum with Gauss’ law in electrostatics

If I use Gauss’ law to calculate the electric field outside of a charged (conducting or insulating) sphere or a point charge, the fields are the same. However, as a test approaches a point charge, the ...
2
votes
2answers
3k views

Electric Field Between Two Parallel Infinite Plates of Positive Charge and a Gaussian Cylinder

Is the electric field between two positively charged parallel infinite plates one with a charge density twice the other effect the electric field on the outside of the plates? I am thinking no, ...
2
votes
2answers
155 views

Newtonian gravity equation in a 2 dimensional world [duplicate]

I am wondering if my line of thought is correct - and thus the resulting answer to the problem above would be correct. As we know the gravitational force (of two point masses) is given by $$F = ...
-2
votes
1answer
614 views

Net flux calculation through a cube [closed]

Ans: Applying Gauss’s law the net flux can be calculated. And for option (B), I guess the flux will be 0. But not sure. Can anyone explain all the 3 options? For left and rignt face, EA = ...
1
vote
0answers
115 views

insulator based gauss law questions

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply. Here's a question I'm working on that isn't part of my book. where the radii ...
0
votes
1answer
478 views

Electric field outside a sphere with a cavity

I have a sphere of radius $2a$ centered at the origin and made of a nonconducting material that has a uniform volume charge density $\rho$. A spherical cavity of radius $a$ eccentric to the right side ...
-2
votes
2answers
107 views

Physical interpretation of $\iiint (∇\cdot\vec E)\mbox{d} V$ [duplicate]

Can anybody explain the physical interpretation of Gauss's law $$\iiint (\nabla\cdot \vec E)~\mbox{d}V~=~\frac{Q}{\epsilon_0}? $$ Also, how is the differential form of Gauss's law obtained from ...
2
votes
2answers
2k views

Flux through side of a cube

I am looking at Griffiths introduction to Electrodynamics 3rd ED. Problem 2.10 asks for the flux of $E$ through the right face of the cube, when a charge $q$ is in the back left corner of the cube. ...
2
votes
1answer
87 views

Intuition behind defining divergence as flux divided by volume?

For a continuously differentiable vector field $F$ the divergence theorem can be used to give $$(\nabla\cdot F)(a) = \lim_{r\to 0} \frac{3}{4\pi r^3}\int_{|x-a|=r} F \cdot n dA$$ This should mean that ...
3
votes
3answers
476 views

Can someone give an intuitive way of understanding why Gauss's law holds?

Gauss' Law of electrostatics is an amazing law. It is extremely useful (as far as problems framed for it are concerned :D. I do not have a real world-problem solving experience of using Gauss' Law). ...
3
votes
2answers
379 views

Potential of arbitrary charge distribution

Imagine this: You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be ...
2
votes
4answers
2k views

The relation between Gauss's law and Coulomb law and why is it important that the electric field decrease proportionally to $\frac{1}{r^{2}}$?

My question relates to the third MIT's video lecture about Electricity and Magnetism, specifically from $21:18-22:00$ : http://youtu.be/XaaP1bWFjDA?t=21m18s I have watched the development of Gauss's ...
3
votes
2answers
168 views

Why is the radial direction the preferred one in spherical symmetry?

I am learning about electricity and magnetism by watching MIT video lectures. In the lecture about Gauss's law, while trying to calculate the flux through a sphere with charge in it, the lecturer ...
1
vote
1answer
1k views

How to find electric scalar potential of infinite wire with Poisson/Laplace equation?

I though it will be easier then calculating the electric field and then integrating, but I am stuck. lets say we have an infinite wire, charged $\lambda$ per unit of length and its located at the ...
1
vote
2answers
307 views

Why is electric flux defined as $\Phi = E \cdot S$?

Flux, as I understand it, is the amount of substance passing through a particular surface over some time. So, from a simple perspective, considering photons that go through some virtual surface $A$ ...