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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. ...
Many times in the use and calculation of electric and magnetic fields, the approach used first computes an associated potential: the electric potential, , for the electric field, and the magnetic vector potential, A, for the magnetic field. The electric potential is a scalar field, while the magnetic potential is a vector field.
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 ...
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. Since the lowest-order term observed in magnetic sources is the dipole term, it dominates at large distances.
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 ...
In the context of special relativity, it is natural to join the magnetic vector potential together with the (scalar) electric potential into the electromagnetic potential, also called four-potential. One motivation for doing so is that the four-potential is a mathematical four-vector. Thus, using standard four-vector transformation rules, if ...
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]
The electric potential and the magnetic vector potential together form a four-vector, so that the two kinds of potential are mixed under Lorentz transformations. Practically, the electric potential is a continuous function in all space, because a spatial derivative of a discontinuous electric potential yields an electric field of impossibly ...