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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. ...
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 ...
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.
λ is the magnetic latitude (equal to 90° − θ) where θ is the magnetic colatitude, measured in radians or degrees from the dipole axis [note 1] m is the dipole moment, measured in ampere-square metres or joules per tesla μ 0 is the permeability of free space, measured in henries per metre.
The electric potential of a point charge q located on the z-axis at = (Fig. 1) equals = = + .. If the radius r of the observation point is greater than a, we may factor out and expand the square root in powers of (/) < using Legendre polynomials = = () = (+) () where the axial multipole moments contain everything specific to a given charge distribution; the other parts of the electric ...
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 ...
In advanced classical mechanics it is often useful, and in quantum mechanics frequently essential, to express Maxwell's equations in a potential formulation involving the electric potential (also called scalar potential) φ, and the magnetic potential (a vector potential) A. For example, the analysis of radio antennas makes full use of Maxwell ...
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]