Questions tagged [coulombs-law]

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

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3answers
67 views

Does the electric field in 1D exist in nature?

This is a question related to: Electric field and electric potential of a point charge in 2D and 1D Let's study in more detail the 1D case. In the 3D case we integrate a sphere of radius $r$ and get $...
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37 views

Arrange $F_1$, $F_2$ and $F_3$ in descending order [closed]

In case 1 the medium is air and Q1 and Q2 are point charges. I thought that force will be inversely related to the dielectric constant so I thought F1>F2>F3 but that's not that the correct ...
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1answer
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In a square ABCD, find the net electrostatic force on the center of square O [closed]

On point A there is a charge of $+q$, on Point B charge of $-q$, on Point C charge of $+2q$, on Point D charge of $-2q$. I did this problem using coulomb's law , and I am not quite sure about the ...
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1answer
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Does Earnshaw's theorem apply to electrostatic + gravitational systems?

I've been learning about particle traps and Earnshaw's theorem. When dealing purely with electrostatic forces the theorem makes intuitive sense to me. But does it really apply to systems involving ...
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1answer
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Gauss law for positive charge densities

I am trying to write a PIC (Particle In Cell) code to simulate plasma physics. I am starting with the simplest case, which is a 1D system with a longitudinal field $E = E(x)$. I am using this article ...
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Electric field outside a full sphere

I'll glad for help how can be proven without using Gauss's law that the electric field outside a sphere with continuous charge distribution equals (when $Q$ is total charge of the sphere and $d$ is ...
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1answer
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When do meet two opposite charges? [closed]

Two opposite charges with the same mass are situated on a frictionless surface. When do they meet if they are freed?
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What conditions are necessary for an inverse square law of a quantity?

Explanations for why forces like gravity obey an inverse square law usually refer to flux lines which decrease in density $\propto \frac{1}{4 \pi r^2}$. However there are many other cases of ...
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2answers
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Doesn't the acquired charge on the insulator also get polarized?

I was wondering that in experiments such as comb attracting tiny paper pieces or a charged balloon sticking to the wall. The comb and balloon acquires negative charge that is localized on the surface ...
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1answer
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Work done in assembling a continuous system having some charge density is always positive

The work done in assembling a continuous system having some charge density is given as the $$W=\frac{\epsilon_{0}}{2} \int E^{2} d \tau$$ which is always positive. Does this mean no matter what ...
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2answers
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Why does the dependence of Coulomb force on the medium not conflict with the superposition principle?

Why does the dependence of Coulomb force on the medium not conflict with the superposition principle? As I have been told (and checked myself on the web including this website), the Coulomb force ...
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1answer
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Electric field a height $z$ above an infinitely long sheet of charge

Consider an infinitely long sheet of charge of width $L$ lying on the $xy$-plane, between $x=-L/2$ and $x=L/2$. The surface charge density is $\eta$. I derive an expression for the electric field $E$ ...
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Is Rutherford scattering formula inconsistent with reality?

On our way to deriving the famous Rutherford scattering formula, we get a formula for the fraction ($f$) of incident alpha particles scattered by $\theta$ or more and this formula has the form $$f=\pi ...
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Why do equations change when we use different unit systems?

Coulomb's law in vacuum is generally stated as $$F = \frac{1}{4\pi\varepsilon_0} \frac{Q_1 Q_2}{r^2}.$$ However, apparently, by going to Gaussian units, $\varepsilon_0$ will take on a value $\frac{1}{...
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What type of electric field different from what is obeyed from Coulombs law is always obeying the Gauss law?

Follow up question from this : How one concludes that Gauss law is valid here or not and line integral of $E$ is zero without using curl? i thought of if electric field is not of form kq/r^2 from a ...
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1answer
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Charge of conductive sphere around charge

Consider suspending a charge inside a conductive sphere: The answers to this question state that there will be a charge of +Q induced on the outside of the sphere (and a charge of -Q on the inside). ...
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3answers
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Loss of energy of an electric field, what does it imply?

Suppose we have a positive electrically charged particle with infinite mass, so it is fixed at one point. We have also a negatively charged particle with finite mass. This second particle will be ...
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3answers
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Potential energy mutually shared

Given there are $2$ non-moving like charges in space. the total energy is the sum of potential energies plus kinetic (zero). The potential energy of charge $A$ due to charge $B$ is $kq_1q_2/r$ and the ...
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Is it OK to Think of Electric Charge as Mass?

Since both are physical properties, is it ok to think of them as if they are the same thing, just in different contexts? Mass affects how much an object experiences gravity in a gravitational field, ...
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1answer
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Determining charge magnitude through comparison with force of tension

Three charges of mass $m$ and charge $q$ are tied to massless ropes of length $l_!$, and hung from a single, fixed point. At equilibrium, the charges form an equilateral triangle in a horizontal plane ...
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Physical interpreation of coulomb and exchange integral

When trying to solve the Schrodinger equation for the electronic hamiltonian: $$H_{el} = \sum_{i=1}^{N} \bigg( - \frac{1}{2}\nabla_i^2 - \sum_A \frac{Z}{r_{i_A}} \bigg) + \sum_{i>j=1}^{N}\frac{1}{...
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1answer
37 views

Divergent electric potential

Consider the electric potential at the rim of a uniformly charged ring/circle of radius $a$ (not a 2D disk) with linear charge density $\lambda$. Take the origin as the centre of a the ring. $$dV=\...
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What are the “derivations” of the inverse-square law?

Besides the derivation mentioned in this Wiki article, I want to know if there exists any other derivation of the inverse-square law based on some profound physical/philosophical concepts.
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Help with the derivation of a variant of Coulomb's Law

My E&M textbook says the following: The electric field at position $r= (x,y,z)$ generated by a point charge $q$ at the origin is given by $$\vec{E}(r) =\frac{q}{4π\epsilon_0r^2}\hat r=\frac{q}{4π\...
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1answer
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Two positive charges $q$ and $3q$ and are a length 10 cm apart [closed]

(a) Where could a third charge be placed so as to experience no net force? The solution is as follows $$ K_e \frac{q_1q_3}{x^2}=K_e\frac{3q_1q_3}{(x-a)^2}$$ I understand you can cancel out the charges ...
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1answer
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Derivation of Coulomb's Law in Higher Dimensions

How could one go about deriving coulomb's law for an $n$-dimensional space. For example, a 9D space (I would like to know how for these higher dimensions)? I know in 3D space the volume and radius ...
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Deriving approximate wave function of virtual photons in a simplified model of momentum transfer [duplicate]

In the virtual particles FAQ here https://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html, under "How can they be responsible for attractive forces?" I didn't follow this step: ...
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1answer
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Why can you not use Gauss law to calculate the electric field a distance $D$ away from a charged cube?

Why can one not use Gauss law to calculate the electric field a distance $D$ away from a charged cube? I have read that the electric field at the face of the cube is not perpendicular or parallel to ...
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In the solution of this problem, why choose the positive square root?

I was solving the following problem: I made it but I got confused by something: I've obtained more solutions than I should. I went to see the solution in hope of clearing it up, the solution is: Now ...
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Force between two point charges lying in different media

Consider, as in the following picture, two point charges $q$ and $Q$, the former lying in (say) air, and the latter in water. The charges cannot move. What is the force exerted by each of the two ...
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1answer
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Identifying variable in an ion thruster problem

recently came across a school revision problem introduced my teacher about ion thrusters. With the assumption that we are ionising air (Nitrogen) and that the ions accelerate by mutual repulsion ...
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How volume of plasma in B That can affect A increases as $r^3$ if we consider effect of two slightly charged region separated by $r$ distance?

In plasma physics by Chen, in the topic collective behaviour, it is written: Let us consider the effect on each other of two slightly charged regions A and B separated by a distance $r$ coulomb force ...
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1answer
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Integral over hemisphere [closed]

I am trying to find the force acting on a charged hemispherical shell from the other half of the sphere. I have an equation for force, but when trying to find only the axial forces (since forces in ...
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1answer
47 views

Clarification on solution from Zangwill

The following problem is on page 67 of Zangwill's electrodynamics: An origin-centered spherical shell [of radius $a$] of infinitesimal thickness has uniform surface charge density $\sigma = {Q}/{4\pi\...
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2answers
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On the collision of two electrons in a particle accelerator

The coulombic force between two charges is $$ F = \frac{k q_{1} q_{2}}{r^{2}} $$ For two negative charges this will be repulsive. From the equation, as $r$ tends to zero the force approaches infinity....
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1answer
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What is the intuition behind why $\vec{E} = \int \mathrm{d}\vec{E}$ works for summing up infinitesimal contributions of electric field?

Say you want to find the electric field, $\vec{E}$, at some point in space, $P$, which is induced by some uniformly charged rod, $Q$, of known length, $L$. What you would do is break this charged rod ...
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1answer
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Ewald summations and series convergence

Does anyone have a explanation of why the direct summation of the coulomb interactions between the ions of a crystal structure which might be conditionally convergent is mathematically allowed to be ...
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1answer
84 views

Where does Coulomb's constant, $k_e$, come from?

I'm familiar with Coulomb's law, $\vec{F} = k_e\frac{q_1q_2}{r^2}$, and know how to apply it (having used it extensively in practice, on exams, etc). I find that the $\frac{q_1q_2}{r^2}$ "part&...
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1answer
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Electric field computation with two point-charges and an infinite conducting sheet [closed]

Coordinates in this question are in metres: An infinitely large conducting metal sheet is located at z=0 (covers the xy plane). Point charge of 20 μC is at (0, 0, 1) and of -10 μC is at (2, 0, 1). ...
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1answer
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Coulomb's Law: Determining the magnitude and direction with three charges as given [closed]

It would be appreciated if someone can confirm if I am in a right path in solving this problem. The problem goes this way. Consider three charges on a coordinate system. Charge $q_1$ = +30 nC is at ...
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1answer
48 views

Net Coulomb Force on a charge in a system

Suppose that there are $n$ charges each at rest and positioned at the vertices of an $n$-sided regular polygon with side length $l$. Each charge has a magnitude of $q$ $C$. Can a general formula be ...
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1answer
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Electric forces in dynamic conditions

The coulomb's law is limited to static charges. This made me think: Is it because the distance is not exactly defined when charges are moving so the dynamic condition isn't very much pertinent to ...
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When do these two point charges meet? [duplicate]

Two point charges in the vacuum (so ignore all frictions). They have opposite signs so they will move towards each other under Coulomb's force. The magnitude of their charges are $q_1$ and $q_2$ ...
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2answers
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What is the cause of electric force?

Electric force is observed during the interaction of two charged objects. What is exactly happening to make this force possible?. Previously, I assumed it may be due to the interaction of the two ...
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1answer
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Superposition Principle and Forces

Why does Griffiths write in his book - "For not only does the force on test charge $Q$ depend on the separation distance $r$ between the charges, it also depends on both their velocities and on ...
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2answers
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How is the Coulomb potential infinity resolved in quantum field theory?

People always says that the infinity of the coulomb potential $V(r)=\frac{k}{r}$ as $r$ approach to zero is resolved in quantum field theory. I would like to know how this is done.
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1answer
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How do two charged insulating spheres separated by a finite distance between their centres interact?

< I was solving problems of electrostatics from "Pathfinder for Olympiad and JEE Advanced Physics" by Arvind Tiwari and Sachin Singh when I encountered this problem. I can understand that the ...
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2answers
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Is equation $1/4πε_0$ in Coulombs law a scalar? Plus a question involving Jefimenko's equations [closed]

Is the equation of $1/4πε_0$ in Coulombs law a scalar? Also, does this equation equate to Coulombs constant? In addition, why does Jefimenko use $H=1/4π...$ in his equations? What is the significance ...
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1answer
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Fourier Transform of Coulomb potential in QFT

I am master student of particle physics and I want to find coulomb potential $V(r)$ from $\tilde{V}(p)$ in Schwartz-Quantum Field Theory and the Standard Model what I have as $\tilde{V}(p)$ from 16....
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Why the force is inversly proportional to the square of distance? [duplicate]

Lesser the distance higher the force of attraction.but why it is the square of distance?And also the reason i guess for this force is the attraction force between atoms ( electrons of one atom and ...

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