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Here, k e is a constant, q 1 and q 2 are the quantities of each charge, and the scalar r is the distance between the charges. The force is along the straight line joining the two charges. If the charges have the same sign, the electrostatic force between them makes them repel; if they have different signs, the force between them makes them attract.
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
The electric field is defined at each point in space as the force that would be experienced by an infinitesimally small stationary test charge at that point divided by the charge. [ 6 ] : 469–70 The electric field is defined in terms of force , and force is a vector (i.e. having both magnitude and direction ), so it follows that an electric ...
By 1785 Charles-Augustin de Coulomb showed that two electric charges at rest experience a force inversely proportional to the square of the distance between them, a result now called Coulomb's law. The striking similarity to gravity strengthened the case for action at a distance, at least as a mathematical model. [12]
The invariant mass of an electron is approximately 9.109 × 10 −31 kg, [80] or 5.489 × 10 −4 Da. Due to mass–energy equivalence, this corresponds to a rest energy of 0.511 MeV (8.19 × 10 −14 J). The ratio between the mass of a proton and that of an electron is about 1836.
Two point charges, one with charge +q and the other one with charge −q separated by a distance d, constitute an electric dipole (a simple case of an electric multipole). For this case, the electric dipole moment has a magnitude p = q d {\displaystyle p=qd} and is directed from the negative charge to the positive one.
We can consider an electron of charge and mass passing a stationary ion of charge + and much larger mass at a distance with a speed . The perpendicular force is Z e 2 / ( 4 π ϵ 0 b 2 ) {\displaystyle Ze^{2}/(4\pi \epsilon _{0}b^{2})} at the closest approach and the duration of the encounter is about b / v {\displaystyle b/v} .
The electron's electric dipole moment (EDM) must be collinear with the direction of the electron's magnetic moment (spin). [1] Within the Standard Model , such a dipole is predicted to be non-zero but very small, at most 10 −38 e ⋅cm , [ 2 ] where e stands for the elementary charge .