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3: Dipole and Quadrupole Moments

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    • 3.1: Introduction
      The maximum torque that the dipole experiences when placed in an external electric field is its dipole moment. This is a vector quantity, and the torque is a maximum when the dipole moment is at right angles to the electric field.
    • 3.2: Mathematical Definition of Dipole Moment
      Previously, we gave a physical definition of dipole moment. I am now about to give a mathematical definition.
    • 3.3: Oscillation of a Dipole in an Electric Field
    • 3.4: Potential Energy of a Dipole in an Electric Field
      The amount of work you would have to do to increase the angle between a dipole on a external field is the potential energy of the dipole.
    • 3.5: Force on a Dipole in an Inhomogeneous Electric Field
      While a dipole in a homogeneous field experiences no net force, but we can see that it does experience a net force in an inhomogeneous field.
    • 3.6: Induced Dipoles and Polarizability
      A charged rod will attract an uncharged pith ball since it induces a dipole moment in the uncharged pith ball, which now has a dipole moment, is attracted in the inhomogeneous field surrounding the charged rod. How may a dipole moment be induced in an uncharged body? Well, if the uncharged body is metallic, then once placed in an electric field, the free electrons are attracted to one end of the metal, leaving an excess of positive charge at the other end; this induces a dipole moment.
    • 3.7: The Simple Dipole
      As you may expect from the title of this section, this will be the most difficult and complicated section of this chapter so far. Our aim will be to calculate the field and potential surrounding a simple dipole.
    • 3.8: Quadrupole Moment
      While a single charge is a scalar quantity, and a dipole moment is a vector quantity, the quadrupole moment is a second order symmetric tensor. It has no net charge and no net dipole moment. Unlike a dipole, it will experience neither a net force nor a net torque in any uniform field. It may or may not experience a net force in an external nonuniform field
    • 3.9: Potential at a Large Distance from a Charged Body
    • 3.10: A Geophysical Example

    Thumbnail: Field of two positive and two negative point charges constituting a non-ideal electric quadrupole. (CC BY-SA 3.0; Geek3 via Wikipedia)

    This page titled 3: Dipole and Quadrupole Moments is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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