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A dipole aligned parallel to an electric field has lower potential energy than a dipole making some ... which is the potential due to applied ...
The resulting torque will tend to align the dipole with the applied field, which in the case of an electric dipole, yields a potential energy of U = − p ⋅ E {\displaystyle U=-\mathbf {p} \cdot \mathbf {E} } .
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 ...
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 nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
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 ...
The electron electric dipole moment d e is an intrinsic property of an electron such that the potential energy is linearly related to the strength of the electric field: U = − d e ⋅ E . {\displaystyle U=-\mathbf {d} _{\rm {e}}\cdot \mathbf {E} .}
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.
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: