A law in Classical Electromagnetism and Newtonian Gravity.

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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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219 views

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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Two capacitor plates with equal positive charges $q$

I read in a book that if both the plates of a parallel plate capacitor are given equal positive charges $q$, then the charges on the facing surfaces will be zero and the charge on the outer surfaces ...
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381 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 ...
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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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61 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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100 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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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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54 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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95 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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52 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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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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37 views

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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41 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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Why the electric field $\vec{E}$ is constant (=position independent) for an infinite 2D sheet of constant charge?

So I'm reading a text on electricity and it talks about using the integral to compute the total charge of a collection of points, which I mostly understand. But then we get to finding the electric ...
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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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27 views

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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1answer
98 views

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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Why $1/r^2$ and not another power of $r$ in Newton's law of gravitation?

My book introduces the force of gravitation as a non-contact force between two bodies of mass $M_1$ and $M_2$ separated by a distance $r$ . Then it says it is directly proportional to the product of ...
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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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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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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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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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1answer
65 views

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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126 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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1answer
36 views

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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1answer
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Charge inside conductor

I know that the $E$ field inside a conductor is zero. What happens if I put a source of charge inside the conductor? Say the conductor was spherical centered on the origin and there exists a charge ...
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1answer
45 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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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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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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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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48 views

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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859 views

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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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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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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2answers
374 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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153 views

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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2answers
846 views

Why doesn't a gaussian surface pass through discrete charges?

I have read that Gaussian surface cannot pass through discrete charges. Why is it so? I have even seen in application of Gauss' Law when we imagine a Gaussian Surface passing through a charge ...
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76 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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104 views

Electric flux of a closed surface, $\Psi = Q $ or $\Phi =\int\vec{E}\cdot d\vec{A}$

I have problem with the equation of electric flux. I use one book of fundamental physics and another book of electromagnetic engineering; the two of them give different equations for electric flux. ...
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Why we cannot use Gauss's Law to find the Electric Field of a finite-length charged wire?

One of my physics books has a nice example on how to use Gauss's Law to find the electric field of a long (infinite) charged wire. However, at the very end of the example, the author ends by saying ...
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Gauss's Law of Electric Field how it actually works? & How Gauss derived it?

I want to know how Gauss derived his equation of Electric Field. Did he derive it from Coulomb's law? I don't think so. Please tell me some details about how this law works? inside a Gaussian ...