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0

From Classical Electrodynamics by JD Jackson Chapter 1 Section I.2 The inverse square law is known to hold over at least 25 order of magnitude in length! Earlier: The laboratory and geophysical tests show that on length scales of order $10^{-2}$ to $10^7$ m, the inverse square law holds with extreme precision. At smaller distances we must turn to ...


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The validity of Coulomb's Law over large distances is equivalent to bounding the mass of the photon. In quantum field theory, where one derives Coulomb's law, if the photon had a mass $m$, then the Coulomb potential gets replaced by the Yukawa potential (in natural units where $\hbar=c=1$ and Gaussian units): $$ \frac{e^{-mr}}{4\pi r}\ , $$ where $m$ is the ...


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As for large distances - it is hard to tell whether Coulomb's law applies with any correction or not. A main restriction on precision tests of Coulombs law at large distances is basically the inverse square distance fall-off of the physical effects. If we take a too small charge, it's strength falls of very quickly beyond measurability. On the other hand, ...


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Coulomb's law becomes invalid at distances of the order of the electron Compton wavelength and smaller, due to vacuum polarization. To first order in the fine structure constant, the electric potential due to a charge q at the origin is given by: $$V(r) = \frac{q u(r)}{r}$$ where $$u(r) = 1 +\frac{2\alpha}{3\pi}\int_1^{\infty}du ...


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Coulomb's Law describes the force between two electrically charged particles. $$|F|=k_e{|q_1q_2|\over r^2}\qquad $$ This equation is valid for ANY distance and the force goes to zero at infinity. This means that theoretically, the Coulomb force exists between all charged particles. Note that two conditions must be satisfied for this equation to hold ...


0

Well... you don't really measure electric/magnetic forces at distances much larger than several meters, but that's because electric potentials are difficult to build up. I guess on the small end, it's a little more difficult, but the strong force is essentially the only force that matters inside of nuclei.


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As many people have already said in their answer, if you ask yourself what is the force between any two charged particles which have some velocities at some time in the frame of reference of the lab, then what you find is the Lorentz force: $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$. Now, the problem is when you try to resolve the dynamics ...


1

Suppose in some reference frame S, we have two stationary charged particles, $q_1$ and $q_2$. The force experienced by the first particle due to the second is given by $\textbf{F}_{12} = k \frac{q_1 q_2}{r^2_{12}} \hat{r}_{12}$, where $k$ is Coulomb's constant, $q_i$ is the charge of the respective particle, $r_{12}$ is the distance between the two ...


0

Lorentz's force is acting on the charge $$F = q(E+v\times B)$$ If the charge is moving in an uniform electric field $E$, there will be no $B$ and the force is $F = qE$. In the case of a non-uniform electric field (e.g. a point charge), the electric field at the charge will change in time and thus, by the Ampere's law, a $B$ will be induced. But usually (in ...


3

Coulomb's law is not precisely true when charges are moving-the electrical forces depend also on the motions of the charges in a complicated way. One part of the force between moving charges we call the magnetic force. It is really one aspect of an electrical effect. That is why we call the subject "electromagnetism." There is an important general ...


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Yes, Coulomb's law is accurate for moving charges. It is applied in, for instance, molecular dynamics simulations.


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Concerning the factor $\frac{1}{2}$: It seems that OP in his classical reasoning only accounted for the Coulomb potential energy $$\tag{1}\langle U\rangle ~=~-k_e e^2 \langle \frac{1}{r} \rangle ~=~-\frac{k_e e^2}{a_0} ~<~0.$$ Here $k_e$ is Coulomb's constant and $a_0$ is the Bohr radius.$^1$ However we should also take the kinetic energy $\langle ...


2

When you take a brass plate of considerable thickness and place it in between two charges, say positive and negative, induction takes place in the brass plate since it is a conductor: the electrons shift to the end near the positive charge while the cations stay near the negative charge. Now, induction occurs in order to make the field outside a certain ...


1

The brass plate is a conductor, so the potential will be the same on both sides. The thickness of the brass plate therefore subtracts from the effective distance between the two charges, making the electric field strength higher in the remaining open space between the charges. This stronger field will cause more force to be experienced by each charge. ...


1

The basics about the direction of force and field comes from the "Fleming's Left Hand Rule" and the "Maxwell's Corkscrew Rule". In addition to these the Lorentz force law, i.e. F=q[E+(vxB)] gives the force on a charge moving through a magnetic and electric field [Neglect E if electric field is absent.] The Biot- Savart Law gives the relation between current ...


4

You just need Maxwell's equations and the Lorentz force law. Coulombs law can be derived from Maxwell's equations.



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