Electric Dipoles in a Constant Electric Field

This Demonstration considers the behavior of electric dipoles in an electric field produced by a pair of infinite parallel plates.
Use the "" slider to set the charge density. Select "single dipole" and use the slider "" to set the charge of the dipole and the slider "" to set the distance separating the charges of the dipole. The angle is chosen randomly. The left-hand panel shows a plot of the potential energy of the dipole, with the red dot indicating the specific value for the given parameters. The right-hand panel shows the plates that produce the electric field and the values of the charge density. Use the sliders to vary the electric field and the charge density of the plates, the potential energy stored in the dipole. The legend shows the torque produced by the electric field on the dipole and the angle between the dipole and the field.
With "many dipoles" you can show the dipoles either as arrows or charge using the "show dipoles as arrows" checkbox.

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DETAILS

A constant electric field is produced by two infinite parallel plates with equal charge densities of opposite sign. The electric field is then given by
,
where is the permittivity of the dielectric. This Demonstration uses the permittivity of air.
An electric dipole consists of two charges and separated by a distance . The dipole moment is given by
,
where is the vector from the negative charge toward the positive charge.
When this dipole interacts with an external electric field, the potential energy is given by
.
This field causes a torque on the electric dipoles given by
.
Acted on by this torque, the dipoles reorient themselves toward the direction of the electric field.
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