A law in Classical Electromagnetism and Newtonian Gravity.

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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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Do relativistic electrons have more charge?

Gauss's law tells us that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. When a charged particle is moving close to the speed of light ...
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Is it possible for a conductor initially, not to have a charge?

Well I'm confused. The thing that was implanted to me is that when I hear about conductors, some charge is present and it can move freely. Now what I want to know is that is it possible for a ...
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Simple question regarding Gauss's electric law

I just read that electric flux=enclosed charge/permittivity. Considering the charge in an enclosed surface is always 0, what is the point in even having this equation? Or is the equation actually ...
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Flux through closed surface

My class teacher says charge kept outside a closed surface will not hold any flux because number of field lines entering are same as number of field lines exiting. But when I imagine sufficiently big ...
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Flux of $E$ through the shaded side

A charge $q$ sits at the back corner of a cube, as shown in Figure. What is the flux of $E$ through the shaded side? One of the solution stated that. Looking at the figure, we notice two ...
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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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Will two touching, neutral conductors in an electric field separate?

If you put two square, neutral conductors in the middle of a uniform electric field such that they are touching, will they separate? I thought yes. When they are touching, as shown in the picture, ...
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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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Is Gauss' law valid for time-dependent electric fields?

The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's ...
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Gauss's law in a uniform charge distribution extending infinitely in all directions

Let us assume the universe filled with positive charge. About a particular point, all the positive charged particles will be symmetrical. Now consider a sphere of radius $r < \infty$ and apply ...
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What would happen if the Earth were hollow?

This is a question of my exam. What would a person experienced if he were put in any point inside the Earth that is hollow (all its mass is concentrated in the surface). Finding the gravitational ...
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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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Why, when and where is Gauss's law applicable?

Why is it said that Gauss's Law is mainly applicable for symmetric surfaces/bodies? Why not for asymmetric surfaces? I want a logical explanation! BTW my teacher said that Gauss's law is ...
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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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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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129 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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Dirac delta function equation intuition and proof [duplicate]

What is the intuition and where should I find proof of this equation (do not know what its name is). It is used to derive Gauss law from Newton equation. $${\nabla \cdot \Bigg ( ...
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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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How would a closed conductor with only 1 layer of (atoms/molecules) behave if a charge is placed inside it?

I have quite a few questions actually related to this . Is it possible to have such a situation practically? If theoretically possible, how would the system behave?
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What is meant by “unique direction” in most of the arguments in application of Gauss' Law?

This term is really bothering me a lot. While explaining the radial direction of electric field of a uniformly charged sphere, my book writes: Notice the use of argument of symmetry. There is no ...
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Gauss' law and external electric flux through a cube: net flux is not zero while the interior charge is 0. What have I done wrong?

Consider a cube with side length $L$ and with its sides parallel to the basis vectors $\vec{i}$, $\vec{j}$ and $\vec{k}$. The $X$ axis goes right through the center of two of its faces. The closest ...
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Capacitance of three plates

I'm sorry if this has been asked before, but here it goes. Consider three parallel plane conducting plates (they can be infinite) and suppose the middle plate has some thickness $\delta$ and the other ...
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Method of image charges [closed]

In an attempt to understand the Method of image charges, I'll try to calculate the total charge on grounded conducting plane - with electric dipole & point charge. Given: Point charge $Q$, ...
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Gauss' Law and area vector

Recently I've been doing some physics exercises on electric and magnetic fields and read up somewhere that the vector area of a closed surface is equal to zero. That made me wonder why, when using ...
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Gauss law for gravitational field

Gauss's law is fundamental law of electrostatics. But Can we apply Gauss's law for Gravitational field also?
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Sphere of electric charge revisited

I am thinking about a sphere of homogeneous charge distribution (see Electric field due to a solid sphere of charge, for example). Here we use a Gaussian surface (blue area) to find the electric ...
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How to approximate trajectories and movement of two oppositely charged particles?

Imagine a single, stationary charged atomic ion, say a Lithium anion or cation (Li+ or Li-). Now imagine another a single free, oppositely charged particle--perhaps an electron or Hydrogen ion ...
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Would a non-conducting body ever acquire a uniform static charge throughout it's volume?

I'm studying electromagnetism and optics in first year and solving a lot of problems involving conveniently symmetrical conducting and non-conducting bodies having various uniformly distributed ...
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Gauss's law and charge on surface

Consider a cone (not necessarily right cone), with a charge $q$ at its apex. Fix its base, and let the vertex be movable. Now suppose we intend to find the flux through the base. Since the flux ...
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52 views

Are $Q1$ and $Q2$ attracted or repelled to the sphere shown in the figure below? [closed]

Can you tell from the image below if Q1 and Q2 are attracted or repelled. Will Q2 only be attracted to the sphere if Q2 is enough bigger than Q1? Will the positive charge inside the shell attract ...
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Potential difference inside charge distributions

Always when I think about potential difference inside a symmetrical charge distribution, I think of it being equal to zero because it's dependent on the field and I imagine the directions of each of ...
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22 views

Shell theorem using Gauss Law

Let me present you my problem: Two spherical shells with radius $R_1$ and $R_2$ ($R_1 < R_2$) and masses $M_1$, $M_2$ are concentric. Calculate the gravitational force $\vec{F_g}$ applied ...
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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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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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How can equipotential planes differ in potential in an uniform field?

I'm trying to solve an exercise that asks me the field strength of an uniform electric field where equipotential planes differ by $1\ \mathrm{V}$ and are $2.5\ \mathrm{cm}$ apart. First of all, I ...
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Ampere's Law and Gauss's Law for EXACT CENTER of Finite Wire: Mathematical Justification [closed]

I have always seen it explained that: Ampere's Law (in integral form) works whenever B is constant around a path, so that you can pull it out of the integral. Similarly, if you can draw a ...
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Electric field due to a charged conductor

I have this grave confusion that I have been having since a while. When we calculate the electric field due to an infinite plane sheet of charge then the answer comes out to be $σ/2ε$. In this case we ...
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1answer
122 views

Divergence Theorem, mathematical approach to Gauss's Law?

Let $D$ be a compact region in $\mathbb{R}^3$ with a smooth boundary $S$. Assume $0 \in \text{Int}(D)$. If an electric charge of magnitude $q$ is placed at $0$, the resulting force field is ...
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573 views

Why inverse square not inverse cube law? [duplicate]

So as I understand, the inverse-square law which shows up in a variety of physical laws (Newton's universal law of gravitation, Coulomb's law, etc.) is a mathematical consequence of point-like ...
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Meaning of negative density

Charge density depends on the area/volume and the amount of charge. Before electromagnetism I used to think of density as being positive only. What is the intuitive meaning of negative density? Does ...
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Electric field in a conductor

Is it always true that the electric field in a conductor is zero? What would happen if I put a very big charge inside an ungrounded hollow conducting sphere like this image? The charges inside the ...
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81 views

How to calculate charge on an internal and external surface of a conductor, due to an internal charge

Having a bit of trouble with a question our first year lecturer has given us to think about. Say we're given a hollow cylinder (the hollow region is central and spherical), made of a conducting ...
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Electric field and flux through a spherical surface inside an uneven hollow charge distribution

Consider a uniformly charged shell and two concentric spherical Gaussian surfaces $S_1$ and $S_2$. ($S_1$ radius is greater than charged shell and $S_2$ radius is less than that of charged shell.) We ...
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52 views

What's the geometry of a gravitational field at the flat end of a cylinder?

Gauss's law is fairly straightforward in explaining the gravitational field strength around the curved sides of a cylinder - but what is the geometry of the field at the flat end? For example, does ...
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54 views

How to calculate Electric Field near a charged conducting surface without Gauss' law?

I have two problems : In every textbook I find the use of Gauss' law in calculation of Electric Field near a charged conducting surface. Can it be calculated without Gauss' law? Suppose while using ...
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116 views

In Gauss's law, why do we use an infinte long wire or long plane to calculate electric field intensity?

In the NCERT textbook of class 12, in the section on applications of Gauss's law, there are three applications. The first application is to calculate the electric field intensity around an infinitely ...
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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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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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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 ...