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A stronger mathematical definition is to use vector algebra, since a quantity with magnitude and direction, like the dipole moment of two point charges, can be expressed in vector form = where d is the displacement vector pointing from the negative charge to the positive charge. The electric dipole moment vector p also points from the negative ...
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 ...
This means that there is no dipole. If an electric field is applied to an insulator, then (for instance) the negative charges can move slightly towards the positive side of the field, and the positive charges in the other direction. This leads to an induced dipole which is described as a polarization.
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.
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 ...
Notably, the electric potential due to an idealized point charge (proportional to 1 ⁄ r, with r the distance from the point charge) is continuous in all space except at the location of the point charge. Though electric field is not continuous across an idealized surface charge, it is not infinite at any point. Therefore, the electric ...
The electric field of such a uniformly moving point charge is hence given by: [25] = () /, where is the charge of the point source, is the position vector from the point source to the point in space, is the ratio of observed speed of the charge particle to the speed of light and is the angle between and the observed velocity of the charged ...
Field lines depicting the electric field created by a positive charge (left), negative charge (center), and uncharged object (right). A field line is a graphical visual aid for visualizing vector fields. It consists of an imaginary integral curve which is tangent to the field vector at each point along its length.