Electric Dipole
An Electric Dipole is a pair of equal and opposite Point Charges separated by a small distance. Electric dipoles have a number of interesting properties.
claimed by Jmorton32 (talk) 02:52, 19 October 2015 (EDT)
Mathematical Models
An Exact Model
An electric dipole is constructed from two point charges, one at position [math]\displaystyle{ [\frac{d}{2}, 0] }[/math] and one at position [math]\displaystyle{ [\frac{-d}{2}, 0] }[/math]. These point charges are of equal and opposite charge. We then wish to know the electric field due to the dipole at some point [math]\displaystyle{ p }[/math] in the plane (see the figure). [math]\displaystyle{ p }[/math] can be considered either a distance [math]\displaystyle{ [x_0, y_0] }[/math] from the midpoint of the dipole, or a distance [math]\displaystyle{ r }[/math] and an angle [math]\displaystyle{ \theta }[/math] as in the diagram.
Then we begin by calculating [math]\displaystyle{ r_+ }[/math] and [math]\displaystyle{ r_- }[/math] the radii from the positive and negative particles to the point [math]\displaystyle{ p }[/math]. In this example, we will assume that the positive particle is closer to [math]\displaystyle{ p }[/math], but its simple to modify this derivation for the opposite case. First, we divide [math]\displaystyle{ r }[/math] into its x and y components, [math]\displaystyle{ r_x = r * cos(\theta) }[/math] and [math]\displaystyle{ r_y = r * sin(\theta) }[/math].
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