A law in Classical Electromagnetism and Newtonian Gravity.

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Gauss law problem [on hold]

Consider a cube in an variable electric field such that there is no charge enclosed by the cube.Say E = ax^(1/2) (where a is constant) (Base of cube is in the xz plane) and its direction is parallel ...
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Gauss' Law and enclosed charge

In Halliday and Resnick, I am asked to find the charge on a drum (a cylinder) given the electric field very close to the drum. In the solutions manual, the author appears to enclose the drum with a ...
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Gaussian surface question: arbitrary wire in a plane

I have a question about the setup in the image below. For the wire with $Q+$, if I draw a Gaussian Cylinder that just encloses the wire (as shown), where $s_1$ is the top surface of the cylinder and $...
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1answer
103 views

What is the significance of the Inverse-square law? [duplicate]

Considering its occurrences in various fields like Electrostatics, Gravitation, Acoustics etc. how does the law bind these topics together?
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Electric field due to a charged irregularly shaped balloon

There is a question in my textbook that says: A rubber balloon is given a charge $Q$ distributed uniformly over its surface. Is the field inside the balloon zero everywhere if the balloon does not ...
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2answers
454 views

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
159 views

Surface bound charge in the electric displacement

In Griffiths, the electric displacement is written with just volume charge density, and that is because, he says, 'we cannot apply gauss law precisely at the surface of a dielectric, for here volume ...
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Electric potential due to surface charge distribution on a conducting sphere

Let's consider a conducting sphere. If we charge the sphere, it is understood that there will form a surface charge distribution such that the surface of the sphere is an equipotential surface $ 0=\...
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1answer
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Proof of integral form of Gauss's Law from Coulomb's law without using differential form of Gauss's Law

The integral form of Gauss's Law is: $$\unicode{x222F}{\vec{E}}\cdot{\vec{dS}}=\dfrac{q}{\epsilon_0}.$$ Is there a direct derivation of it from Coulomb's law without using differential form of Gauss'...
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What does the Dirac delta function physically do while deriving Gauss Law form Coulomb's law?

While doing this derivation, the the source coordinates are mentioned as "$s$" and the coordinate of the point at which field is to be calculated is mentioned as "$r$". Kindly follow this Wikipedia ...
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What moves the charges between capacitors?

Suppose I charged two capacitors to charges Q1 and Q2. By charging a capacitor to charge +Q , I mean that one plate acquires a net charge +Q and another plate acquires a net charge -Q.The capacitors ...
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Gauss Law Question [duplicate]

Why is ${\rm d}\vec{A}_1$ pointing up and ${\rm d}\vec{A}_2$ pointing down? Electric field ${\rm d}\vec{E}_1$ is pointing up so isn't it supposed to be perpendicular to the surface?
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Surface charge outside conductor

If I have a hollow conductor of arbitrary shape, and have a charge placed inside is cavity, then is there anything I can say for sure about the charge distribution on the outer surface? I know that ...
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134 views

Question about Gauss' law and dipoles

I've got a question about dipoles and Gauss' law: Consider an electric dipole $p=ql$ in free space, centred at the origin of a Cartesian reference frame. Using Gauss’s Law, discuss if the electric ...
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55 views

Do any fundamental particles with gravitational or electric dipoles exist?

For magnetism: $$ \oint \vec{B} \cdot \mathrm{d} A = 0 $$ For electricity: $$ \oint \vec{E} \cdot \mathrm{d} A = \frac{Q}{\epsilon_0} $$ For gravity: $$ \oint \vec{g} \cdot \mathrm{d} A = -4\pi G ...
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Difference between $E$ field configuration, sheet of charge: infinite sheet of charge, conducting vs. non-conducting

This is a very easy question, but I often confused myself. Perhaps someone could explain this concept again: A non-conducting infinite sheet of charge has the electric field configuration \begin{...
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1answer
46 views

Derivation Poisson's gravity equation by divergence theorem [closed]

I'm trying deduce the poisson's equation $\nabla^2\Phi (x)=-4\pi G\sigma(x)$ by divergence theorem Let $D:x^2+y^2+z^2\leq 1$ and $\sigma:D\to \mathbb{R}$ be the mass density function of $D$ (suppose ...
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Why Poisson's equation is important?

The Poisson equation can be deduced by Newton's mechanics: $$\Delta \Phi =-4\pi G\sigma$$ Einstein tried to give a "Poisson's equation" that works with his theory. This equation seems to be ...
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155 views

How can electric field representation be obtained from Enge representation using Maxwell's equations?

Suppose we have a long electric capacitor. Let $L$ be its length ($z$ coordinate), $W$ its width ($y$ coordinate), and $D$ its full height (full aperture; $x$ coordinate). Let $L\gg W\gg D$. The ...
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1answer
148 views

Charge distribution on a Gaussian surface

In the text, it is said that the skewed distribution of positive charge on the inner wall cannot produce an eletric field in the shell to affect the distribution of charge on the outer wall. Why? ...
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4answers
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Gauss Theorem:Electric field of an uniformly charged non-conducting spherical shell

I want to know the electric field of an uniformly charged non-conducting spherical shell. I know that in case of conductors(metals),the sphere can be shell or it can be solid,but in both the cases ,...
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5answers
183 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 the ...
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2answers
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Is there something similar to Gauss's Law For Gravity in General Relativity?

In Newtonian Physics there is an equation that for the Gravitational Flux of an object known as Gauss's Law For Gravity. Gauss's Law for Gravity describes the number of Gravitational Field Lines ...
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33 views

Force between the plates of a capacitor

As we know that the electric field between two parallel plates of a capacitor is $$E=\frac{\sigma}{\epsilon_0}$$, so the magnitude of force exerted by one plate on the other should have been $$F=QE$$. ...
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2answers
110 views

Electric flux density between the 2 plates of a capacitor

I am reading a solved exercise about a parallel plate capacitor in which states that the electric flux density between the 2 plates is: $$D=p_{s}$$ where $p_{s}$ is the surface current density of ...
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1answer
116 views

Electric field in a hollow object

I am currently visiting a course about electrodynamics. In my last lecture it was said that if a hollow sphere is inside of a bigger sphere, but only in the bigger sphere there are spherically ...
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36 views

Determination of the electric field of charged object using Gauss's law

when we determine the electric field of a charged rod of infinite length,we consider a circular cylinder to be the gaussian surface for convenience.In the case of a charged sheet we choose the ...
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1answer
72 views

Does changing a closed surface in the manner outlined contradict Gauss' Law?

As I understand it, Gauss' Law states that the electric flux on any arbitrary closed surface is equivalent to the sum of all charges enclosed within the surface times a constant. Mathematically, this ...
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2answers
173 views

The Zero Electric Potential of the “Earth”

I know its the potential differences that matter and generally we define the zero of the electric potential according to our convenience. I would like you to look at this standard problem: Charge $-...
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1answer
37 views

Electric field inside an insulator's cavity [closed]

I'm trying to find the electric field inside insulating sphere's cavity, and I don't know how. However, if there was an conductor I'd know that $E=0$ from Gauss's Law.
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Calculating charge density $\rho(r)$ using Gauss law (both forms)

Below is a question given in my assignment. I tried applying Gauss law in both forms, differential and surface integral form. But both there is a difference by a factor of $2$. Is the differential ...
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3answers
754 views

How to find the distribution of charge on two spheres connected by a conducting wire?

A solid metal sphere of radius $R$ has charge $+2Q$. A hollow spherical shell of radius $3R$, concentric with the first sphere, has net charge $-Q$. What would be the final distribution of the charge ...
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Electric field of an infinite plane (with and without an infinite conductor)

Suppose we have an infinite and uniformly charged (of surface charge density $\sigma \gt 0$) plane at $z = 0$. We can find the electric field at any point $(x, y, z)$ by computing an integral all ...
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Electric Flux in a Cube [closed]

Suppose there are 2 cases: A hollow cube with a point charge $+q$ at the center of one of the faces A hollow cube with a point charge $+q$ at the midpoint of one of the edges. In case 1, the ...
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How to apply Gauss law at null points?

How do I use law to determine total flux at Gaussian surface at null point? It seems , when I consider a Gaussian surface around null point, two axial electric field lines enter it but they don't ...
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48 views

electrical field in coaxial cable

When getting the electric field between the outer and inner cylinder. why is it that we are only concerned with the field generated by the positive charge distribution on the inner surface and not ...
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Electric Flux in a Gaussian Surface

Why is electric flux of a charge everywhere inside a Gaussian Surface constant? I want explanation ( not from any equation ).
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What is the relationship between potential energy and electrical potential?

I actually always thought this was trivial, now I am not so sure. For a potential $\phi$ the potential energy is $V=q\phi$ where q is a test charge. Now I am thinking this may work differently in two ...
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While deriving Coulomb's Law from Gauss' Law, the power of 'r' comes out to be exactly 2 while experiment shows that it differs about 10^(-16). Why?

While deriving Coulomb's Law from Gauss' Law, the power of 'r' comes out to be exactly 2 while experiment shows that it differs about 10^(-16). Why is it so? I'm referring to the book 'Physics by ...
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Calculating the surface integral over a charged box [closed]

In a question that I'm trying to solve, we're told that there is a box with dimensions 20cm long, 4cm high, and 3cm deep. we're given that the electric field on every surface of the box is pointing ...
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Potential difference between point on surface and point on axis of uniformly charged cylinder

Question: Charge is uniformly distributed with charge density $ρ$ inside a very long cylinder of radius $R$. Find the potential difference between the surface and the axis of the cylinder. Express ...
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1answer
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Gauss law and electrostatic induction. Concentric spheres

Imagine you have hollow concentric spheres A and B with radius a and b (b>a), respectively. If A is a conductor and B has a certain density charge, I´ve been taught that B will induce some net charge ...
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96 views

Electric Flux is zero

When is the Electric Flux zero through a closed surface? I know that if number of field lines entering is equal to leaving then it is true. Which I think is always true for a closed surface. So can ...
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4answers
383 views

Electric field on the surface of a charged sphere

We know that the electric field for a point charge is $$ E = \frac{KQ}{R^2}. $$ If $R$, i.e. distance from the electric field producer to the point where we want to find the electric field becomes ...
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2answers
46 views

Electric Field Vector on an insulating solid ball

An insulating solid ball with radius $R$ has a uniform charge density $ρ$. Find the electric field vector inside and outside of the ball if it has dielectric constant $K$. Normally, I'd treat this ...
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3answers
66 views

Spherical Shell with Electric Field Zero Everywhere Inside It

If an isolated, charged spherical shell has a uniform charge distribution, the electric field everywhere inside it is 0, by Gauss' Law. Is the converse true? That is, given an isolated, charged ...
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41 views

Gauss law in dielectrics

How shall we apply Gauss's law for a space such that the volume enclosed by the Gaussian surface have 2 or more mediums with different dielectric constants, such that equal or more than two ...
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52 views

Surface density charge, divergence of the electric field and gauss law

It´s known that the divergence of the electric field at a certain point is given by this formula: $$\nabla \cdot E=\dfrac{\rho (r)}{\epsilon_{0}}$$ Being $\rho (r)$ the volume charge density at that ...
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60 views

Non-Zero Electric Field Inside A Conducting Shell

Statement: "The electric field is zero everywhere inside the conductor, whether the conductor is solid or hollow." Question: A coaxial cable consists of a long, straight filament surrounded by a long,...
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1answer
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Gauss Law with a hollow asymmetric surface

In this video, Walter Lewin argues that no charge will appear on the inside surface of a hollow conductor in electrostatic equilibrium. He uses a Gaussian surface contained entirely within the ...