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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 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 in the system. This fact simplifies calculations significantly, because addition of potential (scalar) fields is much easier than addition of the electric (vector) fields.
The electrostatic potential at point P is ... Given the electrical potential on a conductor surface S i (the equipotential surface or the point P chosen on surface i) ...
A uniform external electric field is supposed to point in the z-direction, and spherical polar coordinates are introduced so the potential created by this field is: = = . The sphere is assumed to be described by a dielectric constant κ , that is, D = κ ε 0 E , {\displaystyle \mathbf {D} =\kappa \varepsilon _{0}\mathbf {E} \,,} and inside ...
The potential V(R), due to the charge distribution, at a point R outside the charge distribution, i.e., | R | > r max, can be expanded in powers of 1/R. Two ways of making this expansion can be found in the literature: The first is a Taylor series in the Cartesian coordinates x , y , and z , while the second is in terms of spherical harmonics ...
A point charge q in the electric field of another charge Q. The electrostatic potential energy, U E, of one point charge q at position r in the presence of a point charge Q, taking an infinite separation between the charges as the reference position, is:
It uses a dimensionless potential = and the lengths are measured in units of the Debye electron radius in the region of zero potential = (where denotes the number density of negative ions in the zero potential region). For the spherical case, L=2, the axial case, L=1, and the planar case, L=0.
Following are some of the several other mathematical formalisms of Maxwell's equations, with the columns separating the two homogeneous Maxwell equations from the two inhomogeneous ones. Each formulation has versions directly in terms of the electric and magnetic fields, and indirectly in terms of the electrical potential φ and the vector ...