A law in Classical Electromagnetism and Newtonian Gravity.

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What is Gauss's Law in two dimensions?

I am trying to figure out how the equation for the field if a Gaussian surface was applied to a 2D plane. I did see another question already asked on the subject, but I didn't get a particular ...
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1answer
144 views

How do you know when you need to use distributions to represent charge densities? [closed]

I tried to solve a problem using Gauss' law in the following way. Let's assume we have a spherical shell of radius $R$ with a charge $Q$ being homogenously distributed on its surface. I am trying to ...
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50 views

Electric field from time varying charge density

Inside a cylinder of infinite length in $z$ axis, there is charge density $ ρ = cos(βz -ωt)$. I want to find the electric field and as far as i can understand we will get a radial component of $E$. ...
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1answer
92 views

How can I apply to the differential form of Gauss' Law? [closed]

I'm trying to learn Maxwell's equations but I got stuck. I couldn't understand the usage of the differential form of the Gauss' law. How can it be applied to questions? For example, let's say there is ...
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2k views

Electric field for two coaxial cylindrical conductors of finite length with Gauss' Law

I'm confused with the Gauss' Law to calculate the electric field for two coaxial cylindrical conductors of finite length. I know that we can use the Gauss' Law to calculate the electric field for two ...
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1answer
860 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 ...
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0answers
189 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 ...
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1answer
6k views

Electric field due to a solid sphere of charge

I have been trying to understand the last step of this derivation. Consider a sphere made up of charge $+q$. Let $R$ be the radius of the sphere and $O$, its center. A point $P$ lies inside the ...
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402 views

What does it mean that a magnetic field's flux vanishes through any closed surface?

I'm reading the Britannica guide to Electricity and Magnetism, and I came across the following quote: A fundamental property of a magnetic field is that its flux through any closed surface ...
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85 views

Help me understand Gauss law

Suppose I have the following, the gaussian surface is the drawing in the middle. So charge enclosed is zero, and then eletric field must be zero since the area of the gaussian surface is not zero. ...
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395 views

Electric Flux - What is the point?

Electric flux is a defined quantity that is proportional to the no. of field lines passing through a given area element for a given electric field. It is not proportional to the relative density of ...
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138 views

Divergence of conservative electric field

I have a little doubt about the following: according Gauss law in the form of Maxwell's equation, we know that: $$ {\rm div} (D)~=~ \rho(v) $$ This just tells us that the electric field has nonzero ...
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93 views

Using Gauss's law (differential form) on an infinite line of charge

I just read about Gauss's law in differential form and how to compute divergence. I worked out the $1/r^2$ field and got zero as expected! I was very happy. Then I thought the infinite line of charge, ...
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136 views

Inverse Square Law and extra space dimensions

Newton's famous Inverse Square Law says that in $n=3$ dimension of space, force is inversely proportional to the square of the distance between a source and a target. I understand that for higher ...
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1answer
826 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 ...
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328 views

Gauss's law… if the integral defining $\boldsymbol{E}$ diverges?

I have been told (here) that, under particular conditions, the electric field produced by a charge present in space $D$, defined by ...
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192 views

Gauss' law in differential form and electric fields

I know Gauss' divergence theorem, according to which $$\iiint_D\nabla\cdot\boldsymbol{F}\text{d}x\text{d}y\text{d}z=\iint_{\partial D}\boldsymbol{F}\cdot\boldsymbol{N}_e\text{d}\sigma$$ where $D$ is a ...
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81 views

Paradox in electrostatics in relation to Gaussian surfaces?

I have encountered something that is very confusing. My problem is this. I am assuming two infinite cubical Gaussian surfaces sharing a common side. One of the cubes contains a charge $q_1$ at a ...
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1answer
2k views

Zero divergence of Electric field

I'm trying to rigorously derive the integral form of Gauss's law from Coulomb's law and the divergence theorem. Arrive at $$ \oint\limits_{\partial V} E\cdot da = \begin{cases} \frac ...
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89 views

Charge inside a sphere

Suppose I have a sphere of radius $r$ with all the charge residing on the surface, distributed uniformly i.e. charge density $\sigma$ is constant. I want to find the electric field created by this ...
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1answer
80 views

Electrostatic field in a Dielectric equations misbehaving

Equation 1: $\int{\vec{E}.\vec{ds}} = \int\frac{\rho_{free} + \rho_{bound}}{\epsilon_0} dv$ (Gauss's Law) Equation 2: $\int{\vec{D}.\vec{ds}} = \int\rho_{free} dv$ (Gauss's Law) , but $\vec{D} = ...
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594 views

Gauss Law for Magnetism,Non Instantaneous Field Propagation

Is the magnetic force instantaneous? And, are all field lines established simultaneously? Otherwise, for example, the field line marked 'L' will take longer time to propagate than the ones above it, ...
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141 views

Why is the flux 0? I don't understand this concept

! Why does it say that the flux due to q_2 and q_3 through S is 0? Doesn't it contain a nonzero charge q_1? Does anyone also know the difference between "no charge" vs "net charge is 0"? My book ...
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52 views

How does a point charge interact with a Gaussian surface?

A spherical Gaussian surface encloses a point charge $q$. The point charge is moved to to a point away from the center of the sphere. Does the electric field at a point on the surface change? ...
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1answer
38 views

Why is it true that Laplace's equation does not hold within the sphere in this case?

Find the average potential over a spherical surface of radius $R$ due to a point charge $q$ located inside. (In this case Laplace's equation does not hold within the sphere) This is a question ...
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68 views

Regarding the proof of Gauss's law

I know that this question has already been asked multiple times but I´m still not getting on the mathematical details behind the answers... So I hope that this question doesn´t get closed. First I ...
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1answer
65 views

Why can center of mass be used in calculating gravity?

Why can gravitational forces be based on the center of mass. Due to the fact that gravity is related to the square of the distance should not the gravitational sum of every particle exceed the force ...
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1answer
69 views

Electric field between capacitors [closed]

A parallel-plate capacitor consists of two parallel, conducting plates of area $A$, separated by a distance $d$. Each carries a charge of magnitude $Q$; positive on one, negative on the other. ...
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3answers
101 views

Is the electric field at a single point inside a charged sphere zero?

Many physics textbooks say, Gauss' law shows that the electric field inside a sphere with uniform charge distribution on the surface equals zero. What I want to know is, do they mean total, ...
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81 views

Electric field of a plate with homogenous charge density

As an example for Gauß Law's application, one can find the calculation of an electric field of a plate with homogenous charge density in nearly every textbook: $$E = \frac{\sigma}{2\epsilon_0}$$ I do ...
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94 views

question about Gauss law

If I have an infinite plate with the surface charge of sigma. I know that my electric field is constant $2\pi\sigma$ (using Gauss's law). If I build the Gaussian surface above the plate the charge ...
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1answer
34 views

where does the term half in the formula of electrostatic potential energy comes from?(system of point charges)

Electrostatic potential energy stored in a system of point charges (from wikipedia) The electrostatic potential energy $U_E$ stored in a system of N charges q1, q2, ..., qN at positions r1, r2, ...
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247 views

Wait… why exactly does farady's ice pail experiment prove Gauss's law?

You'll notice there are no equations in this: that's because this is a question of morale, not of math. But a humble one at that! I come to learn, not to expound. But don't let that limit the form ...
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118 views

Gauss's law not making sense

If we have a point charge and outside of it we have a non-conducting Gaussian sphere, then Gauss's law says that the net flux should be zero. I agree that the total field lines coming in are equal to ...
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851 views

Electric field around two charged hollow cylinders

There are two hollow cylinders with same lengths "l" as shown in the figure below. The smaller inner cylinder is negatively charged. The outer one is now induced to become positively charged. I am ...
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1answer
73 views

Help regarding understanding derivation of electrostatic potential in a solution to a problem

I was looking at the solution of finding the energy stored in a charged solid sphere in which the electric field was and then later stated the electrostatic potential is I understand that to ...
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2answers
93 views

Confusion about Gauss's law for Electrostatics

I just learning about Gauss's law in integral and differential form. There's something I'm a bit confused about: Let $\vec{r}$ be the location of your test charge with respect to the origin, and ...
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1answer
57 views

Is the charge of an ion evenly distributed?

This question relates to: Gauss' law and ions? Is the charge distribution in an ion spherically symmetric due to quantum mechanical effects or do we assume it when using Gauss's law, as in the ...
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2k views

Gauss’s Law inside the hollow of charged spherical shell

Use Gauss’s Law to prove that the electric field anywhere inside the hollow of a charged spherical shell must be zero. My attempt: $$\int \mathbf{E}\cdot \mathbf{dA} = \frac{q_{net}}{e}$$ $$\int E ...
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479 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, ...
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110 views

1 charge at the center and many uniformly distributed on the surface of a perfect ideal conducting solid sphere

Suppose there is a perfect ideal conducting solid sphere. Suppose somehow a charge of $+Q$ is kept exactly at the center of the sphere and its surface is also given a $+Q$ charge uniformly distributed ...
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8k 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 ...
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1answer
2k views

Electric field around charged cylinder

This is a homework question, so please don't give me the answer outright. I just need help conceptually. "A cylindrical shell of length 190 m and radius 4 cm carries a uniform surface charge density ...
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2answers
493 views

Proof that flux through a surface is independent of the inner objects' arrangement

$$\Phi=\iint_{\partial V}\mathbf{g} \cdot d \mathbf{A}=-4 \pi G M$$ Essentially, why is $\Phi$ independent of the distribution of mass inside the surface $\partial V$, and the shape of surface ...
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1answer
430 views

Finding the electric field on a point (x,y,z) using Coulomb's Law

Using Gauss' Law, the answer is $$\frac{Q}{4 \pi \epsilon R^2}.$$ However if I were to do the integration using Coulomb's Law, I get $$ \int_0^{2\pi} \int_{0}^{\pi}\int_r^a \frac{\rho \sin\theta dR ...
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1answer
829 views

Gravity force strength in 1D, 2D, 3D and higher spatial dimensions

Let's say that we want to measure the gravity force in 1D, 2D, 3D and higher spatial dimensions. Will we get the same force strength in the first 3 dimensions and then it will go up? How about if ...
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33 views

Charge outside a Sphere given charge density

If a sphere has a charge density of $\rho =\alpha r^2$, I want to calculate the Electric field outside of the sphere. Starting with Maxwell's equation $\bigtriangledown\cdot E=\frac{\rho }{\epsilon ...
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1answer
43 views

Couple of questions about Gravitational field of an infinite plane

Is it possible to find the gravitationaal field without using infinite integrals or Gauss's law? I would like to know if so because I haven't learnt doing infinite integrals or using Gauss's law yet. ...
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4answers
62 views

Charge inside a charged spherical shell

If I were to put a negative charge inside a negatively charged spherical shell, will it move to the center? Electric field inside the shell due to the shell is zero (Gauss's Law), would that mean ...
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1answer
45 views

Electric flux density for a hollow cylinder using Gauss's law [closed]

In the textbook of "Engineering Electromagnetics": I understood it except the part highlighted with yellow(i.e. how did he find the charge distribution of the outer cylinder? What are the ...