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Questions tagged [coulombs-law]

A fundamental and empirical law quantifying the electrostatic force between two charges.

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For which energetic reasons are ions blocked by cell membranes?

The permeability of cell membranes is given by the following diagram from the book "Biochemistry": The reason that ions get blocked can be explained chemically: The ions favor interactions with the ...
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3answers
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Problems in electrostatic [on hold]

Electrostatic is the branch of physics in which we study about charges at rest relative to inertial reference frames then how can the problems like electron revolving around nucleus be given in this ...
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+50

How to write the Rutherford differential cross section in terms of the momentum transfer?

The Rutherford differential cross section is: $$\frac{d\sigma}{d\Omega} = \frac{Z^2 \alpha^2}{4E^2 \sin^4 (\theta/2)}.$$ I need to write this in terms of the momentum transfer $\frac{d\sigma}{d(Q^...
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Why is it that forces like gravity and electricity (approximately) basically act between pairs of bodies only?

In classical mechanics, with the limit of little movement (so no relativity, waves, and/or "magnetic" effects), we can see that gravitation and electricity can both be described as "two-body" forces, ...
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Electric Potential: Building system of point charges

How can we prove that the amount of work we have to do to build a system of point charges is same , whether we place the point charges one by one or all at once
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1answer
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Electric force between two hemispheres of different radii? [closed]

Two hemispherical thin shells made of insulating materials are concentrically arranged in a free space as shown. The radii of the smaller and larger hemispheres are ‘R’ and ‘2R’ and they carry ...
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Is the direction of the Coulomb force at short distances indeterministic?

Suppose we have two electrons that apply a Coulomb force on each other. At large distances, we can consider the two electrons as point charges and the direction of the Coulomb force would be on the ...
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2answers
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Electrostatic values where there are some charge

I've started asking myself: What is the value of the electric field at the surface of a shell with uniform distribution? In particular, is it infinite, as this point is over an (infinitesimal) ...
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When was Coulomb's constant made/established?

Charles-Augustin de Coulomb lived from 14 June 1736 – 23 August 1806. Coulomb's constant is $$k_{\text e}=\alpha\frac{\hbar c}{e^2},$$ a form of Planck's constant is included, but Max Planck lived ...
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Is this a valid explanation for why charges in a conductor move to the outer surface?

This is a drawing of a spherical conductor with a hollow center. The black dots represent +ive charges, and the arrows represent their electric fields. I am assuming the black dots start on the inner ...
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3answers
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Can the electrostatic force be infinite in magnitude? [closed]

The magnitude of the electrostatic force between two charges $Q$ and $q$ separated by a distance $r$ is given by $$F=\frac{kqQ}{r^2}$$ but the minimum value of $r$ must be $10^{-15}\ \rm m$. Therefore,...
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How did Coulomb measure charges?

I was studying some Electrodynamics when suddenly this question popped into my mind : The whole of Electrodynamics is based on the Coulomb's Law. There is no derivation of this law because it is an ...
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34 views

Quantifying potential energy

As per the definition of potential energy we kept a fixed charge, and in the presence of an electric field of the fixed charge, we release another charge of the same sign moving towards the fixed ...
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787 views

Doubts in understanding some concepts of potential energy

Let us consider a system of charges in space. The potential energy of the system of charges is determined by the amount of work done by the external force to assimilate the charges in that manner. But ...
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1answer
50 views

Why isn't electric potential infinite?

In my textbook, I've read that electric potential is the work performed to carry one unit of positive charge to electric field from infinite distance. We know that, W = Fs So here the distance is ...
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1answer
64 views

Integrating Laplace's equation over a sphere

The Wikipedia page on Laplace's equation states that if the Laplacian of $u$ is integrated over any volume that encloses the source point, $$\iiint_V \nabla \cdot \nabla u \, d^3V =-1.$$ I can'...
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1answer
51 views

How do we know how much charge is in an object?

It's a little science history question but I really wonder how did peoples measured the amount of charge in an ball or something or like in coulombs case how did he measured the electrical force ...
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1answer
99 views

Coulomb's Law Question

The presentation of Coulomb's Law in various books occasionally has a note that the test charge, q2, must be small enough that it doesn"t alter the field of the first charge, q1. The same limitation ...
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1answer
106 views

Why is the electrostatic energy of a nucleus proportional to $Z(Z-1)$?

The complete binding energy is (more details in Krane's book, page 68): $$B = a_v A - a_s A^{2/3} - a_c Z(Z-1)A^{-1/3} - a_{sym} \frac{(A-2Z)^2}{A} + \delta$$ I want to explain the $Z(Z-1)$ term. ...
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When does a vector component keep being a vector, exactly?

English is not my native language, so please forgive my errors. Consider this example: This is a classic: an exercise requiring you to calculate the electric field produced by a charged ring on its ...
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coulomb interaction on a ring

My qualitative understanding is that the mathematical form of the interaction between particles is constrained by their gauge symmetry, so that, for example, the U(1) gauge symmetry in QED gives rise ...
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3answers
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Does the existence of electrons validate the integral form of electric fields?

For an arbitrary charged object, it seems to be the case that we express it as a continuous sum (sum on the reals/integral) of point charges $dq$ that have a canonical Coulomb's law force. That is to ...
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2answers
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What is the unit vector in electric field formula? [duplicate]

What is the $\hat{r}$ (vector) in the formula $\vec{E} = k\frac{q}{r^2} \hat{r}$ for the electric field ? Why we dont use the vectors $\vec{i},\ \vec{j},\ \vec{k}$? Also why this vector doesn't ...
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92 views

Why is Coulomb's force law a $1/r^2$ dependence, while the Coulomb potential has a $1/r$ potential?

My source of confusion comes from reading the following except from my general chemistry textbook, "The energy of interaction between a pair of ions can be calculated using Coulomb's law" $$V = \...
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3answers
90 views

Do real electrons solve the Thomson Problem?

The question of how $N$ electrons (seen as point charges) on a conducting sphere will arrange themselves in the electrostatic final state was first posed by J.J. Thomson in 1904--hence, aka the ...
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1answer
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Electric field of two equal charges of the same sign [closed]

Two equal positive charges are at distance d, -d from the origin on the y axis. What is the distance on the x axis beyond which a small perturbation in y will move a particle away from the x axis? ...
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2answers
71 views

Is the zero distance limit of Coulomb's law something to worry about?

Coulomb's law fails when the distance $r$ between to point charges vanishes. As $r\to 0$, the electric field between two point changes increases without limit. I should be bothered about the limit $r\...
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1answer
120 views

Gauss theorem and inverse square law [duplicate]

I know that the gauss law states that the Flux of the electric field through a closed surface is Q/ε , but does the gauss theorem works also for non inverse square law Fields?
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3answers
124 views

How to find electric field at a point on an arbitrary surface charge $(\sigma)$ due to it?

Electric field at any point due to any volume charge $(\rho)$ Electric field at a point outside a volume charge is given by Coulomb's law: $$\vec{E}=k \iiint_V \dfrac{\rho}{r^2} (\hat{r})dV \tag1$$ ...
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1answer
152 views

Coulomb's Law modified in general relativity?

It seems difficult to track down a clear explanation of this statement: So although the Coulomb law was discovered in a supporting frame, general relativity tells us that the field of such a charge ...
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When and why does the superposition principle of Coulomb's law fail to hold?

In this lecture, Professor Shankar Ramamurthi says that the superposition principle for force vectors of Coulomb's Law is experimentally observed and is not a product of logical analysis. In fact, the ...
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Can radio waves be detected using a coulomb torsion balance?

Radio waves are almost everywhere. shouldn't the coulomb torsion balance be sensitive to any passing through the device?
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(Two fixed charges add in a third), why does it matter which side I put the third charge if I change signs accordingly?

So the question is "Two charges, 1.0 micro-Coulombs and -3.0 micro-Coulombs, are 10 cm apart. Where can a third charge be located so that no net electrostatic force acts on it?". Now the instructor ...
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3answers
67 views

Electrostatics fundamentals

Suppose a charge is kept at the centre of a square frame and the vertices of the frame have four more charges fixed to the frame which are identical to each other but not necessary that these four are ...
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1answer
243 views

Electric force is stronger than gravitational force yet gravitational forces holds the Sun and planets in their orbits around the Sun [closed]

The electric force between an electron and a proton, between two electrons, or between two protons is much stronger than the gravitational force between any of these pairs of particles. Yet even ...
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1answer
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Functions unbounded at a point on the domain: How to show electric field exists for any continuous volume charge density?

My understanding after reading Mike Stone's answer: \begin{align} \vec{E} &= k \iiint_{V} \dfrac{\rho(x',y',z')[x-x'\hat{(i)}+y-y'\hat{(j)}+z-z'\hat{(k)}]}{[(x-x')^{2}+(y-y')^{2}+(z-z')^{2}]^{...
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4answers
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Does Coulomb's law hold as long as $\dot{\rho} = 0$?

Does Coulomb's law, $$\textbf{E}\left(\textbf{r}\right) = \frac{1}{4\pi\epsilon_0}\int \rho\left(\textbf{r}'\right)\frac{\textbf{r} - \textbf{r}'}{\left|\textbf{r} - \textbf{r}'\right|^3}dV',$$ hold ...
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1answer
67 views

Earnshaw's theorem and stability of charge inside a hollowed cavity of conductor

When a positive charge q is placed in the center of a spherical cavity of a spherical neutral conductor, it induces a negative charge $q$ to line the inner wall of the conductor, and a positive charge ...
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1answer
127 views

What is the mathematical reasoning behind the inverse square law of two charges?

The Hon. Henry Cavendish performed an experiment with two spheres, by which he proved that no electric force is produced inside a hollow charged sphere. In other words, proving that no electric field ...
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0answers
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A solution of an electrostatic problem without definition of flux

I have this problem: The figure shows the electric field lines around a system of three charges $q_1$, $q_2$ and $q_3$. The central charge have a value of $q_2=-10.0\,\mu\mathrm C$. Find the value of ...
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2answers
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What is the fundamental explanation for the existence of Electrostatic force?

To explain my question in a better way I will first talk about gravitation! Gravity is not a force and the effects of gravity are ascribed to spacetime curvature My comments: Gravity was explained ...
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1answer
72 views

Is there a higher-level reason why $\nabla\cdot(\hat{\bf r}/r^2) = 0$ in three dimensions but not two? [duplicate]

I am working through Griffiths, Introduction to Electrodynamics, and finding the divergence of the electric field generated by a single charge sitting at the origin. $$\mathbf{E}(\mathbf{r}) = \frac{\...
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1answer
198 views

Fourier tranform of Coulomb-like potential $1/|r-r'|$

I've found that Fourier transform of Coulomb potential $V= q/r$ is $F[V]= 4\pi q/k^2$. Now I need to calculate fourier transform of function $1/|r-r'|$. And I exactly don't know how to operate with ...
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1answer
30 views

Force of electric charges

For the image below, lets say the top charge is 5C and the bottom 1C. And consider this observation frozen at $t=0$, consider an imaginary horizontal line between the 2 charges denoting the centre of ...
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2answers
249 views

Why is the divergence of electric field equal to $\rho \over \epsilon_0$ in electrodynamics?

These two equations are true in electrostatics/magnetostatics: $$\nabla \cdot \vec{E}= {\rho \over \epsilon_0},$$ $$\nabla \cdot \vec{B}=0.$$ I have learned that they are also true in electrodynamics....
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2answers
87 views

Can $E=\frac{q}{4\pi\epsilon_0 r^2}$ be directly derived from differential form of Maxwell equations?

The electric field of a point charge $q$ is well known to be $$\mathbf E=\frac{q}{4\pi\epsilon_0 |\mathbf r|^3}\hat{\mathbf r}$$ This can be derived easily from integral form of Gauss’s law. Taking $...
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1answer
42 views

Solving dynamics of two oppositely charged particles without using energy conservation

Two charges, each $+q$, are separated by distance $d$. One of the charges is fixed, and the other is free to move under the influence of the force from the first. The second particle is initially at ...
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1answer
220 views

Can the Earth's negative charge make negatively charged objects levitate?

Since the earth's surface has a negative charge, could it repel a large highly negatively charged body? An example is an object on stilts carrying a negative charge that is heavier than air, maybe ...
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2answers
72 views

Interaction of charges [duplicate]

As it is known in Physics, two point-size charges (say two electrons) interact with each other through em forces. How this is happening? do they exchange photons? And if so, then do they exchange ...
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2answers
197 views

Why does Coulomb's law hold only for two point charges? [closed]

What is the condition for validation of Coulomb's Law?