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The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system: that is, a measure of the system's overall polarity. ...
In physics, a dipole (from Ancient Greek δίς (dís) 'twice' and πόλος (pólos) 'axis') [1] [2] [3] is an electromagnetic phenomenon which occurs in two ways: An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system is a pair of charges ...
Classical mechanics explores concepts such as force, energy, and potential. [3] Force and potential energy are directly related. A net force acting on any object will cause it to accelerate. As an object moves in the direction of a force acting on it, its potential energy decreases. For example, the gravitational potential energy of a ...
The electrostatic potential energy U E stored in a system of two charges is equal to the electrostatic potential energy of a charge in the electrostatic potential generated by the other. That is to say, if charge q 1 generates an electrostatic potential V 1 , which is a function of position r , then U E = q 2 V 1 ( r 2 ) . {\displaystyle U ...
Each term in the expansion is associated with a characteristic moment and a potential having a characteristic rate of decrease with distance r from the source. Monopole moments have a 1/r rate of decrease, dipole moments have a 1/r 2 rate, quadrupole moments have a 1/r 3 rate, and so on. The higher the order, the faster the potential drops off.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Position vectors r and r′ used in the calculation. The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: =, = where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator. [2]
Since the integral equals the complex conjugate of the interior multipole moments of the second (peripheral) charge distribution, the energy formula reduces to the simple form = = = For example, this formula may be used to determine the electrostatic interaction energies of the atomic nucleus with its surrounding electronic orbitals.