Torque on a Dipole

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The Torque on a Dipole calculator computes the torque based on the charge, distance between dipoles, the magnitude of the electric field and the angle difference between the dipole axis and the magenetic field.

INSTRUCTIONS: Choose units and enter the following:

(L) Distance Separating Dipoles
(q) Charge of the Dipole
|E| Magnitude of Electric Field
(θ) Angle between the axis of the dipoles and magnetic field

Torque on a Dipole (τ): The torque is returned in newton meters (N_m). However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula of the torque on dipole is:

`tau=L*q*|E|*sintheta`

where:

τ = total torque on the dipole
L = distance between poles
q = charge
|E| = magnitude of external field
θ = Angle of the external field with respected dipole.

The following description of torque on a dipole is from Chapter 22.3 Electric Fields of Light and Matter by B. Crowell referenced below.

What determines the torque on a dipole placed in an externally created field? Torque depends on the force, the distance from the axis at which the force is applied, and the angle between the force and the line from the axis to the point of application. Let a dipole consisting of charges +q and -q separated by a distance L be placed in an external field of magnitude |E|, at an angle θ with respect to the field. The total torque on the dipole is

`tau=(L/2)q|E|sintheta+(L/2)q|E|sintheta`

`tau=L*q*|E|*sintheta`.

(Note that even though the two forces are in opposite directions, the torques do not cancel, because they are both trying to twist the dipole in the same direction.) The quantity Lq is called the dipole moment, notated D. (More complex dipoles can also be assigned a dipole moment --- they are defined as having the same dipole moment as the two-charge dipole that would experience the same torque.)

References

22.3 The electric field by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.