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For a spatially uniform electric field across the small region occupied by the dipole, the energy U and the torque are given by [2] =, =. The scalar dot " ⋅ " product and the negative sign shows the potential energy minimises when the dipole is parallel with the field, maximises when it is antiparallel, and is zero when it is perpendicular.
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 ...
It follows that the dipole-dipole interaction goes as the inverse fourth power of the distance. Suppose m 1 and m 2 are two magnetic dipole moments that are far enough apart that they can be treated as point dipoles in calculating their interaction energy. The potential energy H of the interaction is then given by:
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. The discovery of a substantially larger electron electric dipole moment would imply a violation of both parity invariance and time reversal invariance. [3] [4]
Note that, in contrast to the magnitude of an electric field due to a point charge, the electric potential scales respective to the reciprocal of the radius, rather than the radius squared. The electric potential at any location, r , in a system of point charges is equal to the sum of the individual electric potentials due to every point charge ...
A force field is the collection of parameters to describe the physical interactions between atoms or physical units (up to ~10 8) using a given energy expression. The term force field characterizes the collection of parameters for a given interatomic potential (energy function) and is often used within the computational chemistry community. [50]