Questions tagged [coulombs-law]
A fundamental and empirical law quantifying the electrostatic force between two charges.
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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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0answers
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Problem in Electrostatics [closed]
Two point positive charges $q$ each are placed at $( - a,0 )$ and $(a, 0)$. A third charge $q_o$ is placed at $(0, y)$. For what value of $y$ is the force on $q_o$ maximum ?
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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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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
48 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
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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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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
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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
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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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3answers
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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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0answers
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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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3answers
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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"
$$V = \...
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3answers
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Do real electrons solve the Thomson Problem?
The question of how $N$ electrons (seen as point charges) on a conducting sphere will arrange themselves in the electrostatic final state was first posed by J.J. Thomson in 1904--hence, aka the ...
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1answer
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Electric field of two equal charges of the same sign [closed]
Two equal positive charges are at distance d, -d from the origin on the y axis. What is the distance on the x axis beyond which a small perturbation in y will move a particle away from the x axis?
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2answers
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Is the zero distance limit of Coulomb's law something to worry about?
Coulomb's law fails when the distance $r$ between to point charges vanishes. As $r\to 0$, the electric field between two point changes increases without limit. I should be bothered about the limit $r\...
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1answer
76 views
Gauss theorem and inverse square law [duplicate]
I know that the gauss law states that the Flux of the electric field through a closed surface is Q/ε , but does the gauss theorem works also for non inverse square law Fields?
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3answers
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How to find electric field at a point on an arbitrary surface charge $(\sigma)$ due to it?
Electric field at any point due to any volume charge $(\rho)$
Electric field at a point outside a volume charge is given by Coulomb's law:
$$\vec{E}=k \iiint_V \dfrac{\rho}{r^2} (\hat{r})dV \tag1$$
...
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1answer
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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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0answers
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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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2answers
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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
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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
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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',$$
hold ...
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1answer
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Earnshaw's theorem and stability of charge inside a hollowed cavity of conductor
When a positive charge q is placed in the center of a spherical cavity of a spherical neutral conductor, it induces a negative charge $q$ to line the inner wall of the conductor, and a positive charge ...
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1answer
107 views
What is the mathematical reasoning behind the inverse square law of two charges?
The Hon. Henry Cavendish performed an experiment with two spheres, by which he proved that no electric force is produced inside a hollow charged sphere. In other words, proving that no electric field ...
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0answers
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A solution of an electrostatic problem without definition of flux
I have this problem:
The figure shows the electric field lines around a system of three charges $q_1$, $q_2$ and $q_3$. The central charge have a value of $q_2=-10.0\,\mu\mathrm C$. Find the value of ...
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2answers
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What is the fundamental explanation for the existence of Electrostatic force?
To explain my question in a better way I will first talk about gravitation!
Gravity is not a force and the effects of gravity are ascribed to spacetime curvature
My comments:
Gravity was explained ...
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1answer
68 views
Is there a higher-level reason why $\nabla\cdot(\hat{\bf r}/r^2) = 0$ in three dimensions but not two? [duplicate]
I am working through Griffiths, Introduction to Electrodynamics, and finding the divergence of the electric field generated by a single charge sitting at the origin.
$$\mathbf{E}(\mathbf{r}) = \frac{\...
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1answer
130 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
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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
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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
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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
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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
165 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
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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
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Why does Coulomb's law hold only for two point charges? [closed]
What is the condition for validation of Coulomb's Law?
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1answer
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Are two charges attracting each other constantly accelerating?
Using Coulomb's Law: $\frac{k_eq_1q_2}{r^2}$, say we have $2$ charges of $1\ \rm C$ each, separated by a distance of $1\ \rm m$. The force would be $8,987,551,787.3681767\ \rm N$, considering $k_e = ...
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1answer
66 views
Can I trap mosquitos with Coulomb's force? [closed]
Can I fill a metallic conductor with a very large positive charge, attach it with a insulator to a wall, put it near a window under the sun (visible light and UV in order to cause it to expell ...
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0answers
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Deducting from a special case that the electric field transforms as a 2nd rank tensor: Vanishing divergence concludes vanishing vector field?
I'm (as in the previous question) still working with Kobe's Paper. I try to understand his reasoning (given in Appendix A) why the electric field components should be components of a 2nd rank tensor. ...
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2answers
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What is the physical meaning of the Fourier transformed Coulomb potential $1/q^2$?
$V(r)=\frac{1}{r}$ means for any two electrons at position $r_1$ and $r_2$, the electric potential is given by $\frac{1}{|r_1-r_2|}$
The Fourier transform of $\frac{1}{r}$ is $\frac{1}{q^2}$.
How ...
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4answers
783 views
Does a point charge inside a conducting shell cause redistribution of charge in the shell?
A point charge Q is placed inside a conducting spherical shell at a random place (non-centre).
I have read that there is no force on Q from the shell no matter where Q is inside the shell ('there ...
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1answer
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Cavendish's experiment on concentric conducting shells
In a paper were there was a section addressing Cavendish's experiment on concentric conducting shells which was basically the following : Two conducting spherical shells were put together (like the ...
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4answers
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Can Newton’s law of gravitation be derived from Coulomb’s law? [duplicate]
I’m casually learning physics and have noticed that Newton’s law of gravitation and the electrostatic force formulas look similar. I’ve asked this question before but would really appreciate another ...
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2answers
118 views
According to Coulomb law, why do fixed charges interact, if they don't emit the photons?
Why does it happens, if fixed charges don't oscillate the em field?
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1answer
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Why there is a distance dependence in Coulomb's law if photons can travel to infinity?
Why there is a distance dependence in coulombs law if photons can travel to infinity? Why there is distance dependence at all?
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how the energy values of different landau levels depend on B field (quantum dot)
I came across a remark that "states in the first landau level fall in energy with increasing B, while those in the second landau level rise here. The book seems to be getting this from this paper. (...
