dipole moment

Examples of dipole moment in the following topics:

• Dipole Moments

  • The electric dipole moment is a measure of polarity in a system.
  • There are many different types of dipole moments, including electric dipole moments, magnetic dipole moments, and topological dipole moments.
  • Among the subset of electric dipole moments are transition dipole moments, molecular dipole moments , bond dipole moments, and electron electric dipole moments.
  • For the purposes of this atom we will focus on a broad overview of electric dipole moment in static situations.
  • Relate the electric dipole moment to the polarity in a system

• A Physical Aside: Multipole Radiation

  • It is possible to calculate the radiation field to higher order in $L/(c\tau)$.This is necessary if the dipole moment vanishes, for example.
  • where $k\equiv\omega/c$$n=0$ gives the dipole radiation, $n=1$ gives the quadrupole radiation and so on.

• Ferromagnetism

  • Ferromagnetism arises from the fundamental property of an electron; it also carries charge to have a dipole moment.
  • This dipole moment comes from the more fundamental property of the electron—its quantum mechanical spin.
  • However, in materials with a filled electron shell, the total dipole moment of the electrons is zero, as the spins are in up/down pairs.
  • Only atoms with partially filled shells (i.e., unpaired spins) can have a net magnetic moment.
  • (According to Hund's rules, the first few electrons in a shell tend to have the same spin, thereby increasing the total dipole moment. )

• Polarization

  • This separation creates a dipole moment, as shown in .
  • On the molecular level, polarization can occur with both dipoles and ions.
  • One example of a dipole molecule is water, (H2O), which has a bent shape (the H-O-H angle is 104.45°) and in which the oxygen pulls electron density away from the H atoms, leaving the H relatively positive and the O relatively negative, as shown in .
  • Water is an example of a dipole molecule, which has a bent shape (the H-O-H angle is 104.45°) and in which the oxygen pulls electron density away from the H atoms, leaving the H relatively positive and the O relatively negative.
  • The atom's dipole moment is represented by M.

• Total Polarization

  • The physical mechanism for this can be qualitatively understood from the manner in which electric dipoles in the media respond to p-polarized light (whose electric field is polarized in the same plane as the incident ray and the surface normal).
  • One can imagine that light incident on the surface is absorbed, and then re-radiated by oscillating electric dipoles at the interface between the two media.
  • The refracted light is emitted perpendicular to the direction of the dipole moment; no energy can be radiated in the direction of the dipole moment.
  • Thus, if the angle of reflection θ1 (angle of reflection) is equal to the alignment of the dipoles (90 - θ2), where θ2 is angle of refraction, no light is reflected.

• Spectrum of Synchrotron radiation

  • If the electron is non-relativistic its dipole moment varies as $e^{i\omega_B t}$ so we would expect radiation at a single frequency $\omega_B$.

• Radiation from Systems of Particles

  • Let's examine the spectrum of dipole radiation.
  • To make things easier, let us assume that the dipole lies in a single direction and varies in magnitude (imagine a negative charge moving up and down a wire).

• Paramagnetism and Diamagnetism

  • The magnetic moment induced by the applied field is linear in the field strength; it is also rather weak.
  • Constituent atoms or molecules of paramagnetic materials have permanent magnetic moments (dipoles), even in the absence of an applied field.
  • Generally, the permanent moment is caused by the spin of unpaired electrons in atomic or molecular electron orbitals.
  • In pure paramagnetism, the dipoles do not interact with each other and are randomly oriented in the absence of an external field due to thermal agitation; this results in a zero net magnetic moment.
  • When a magnetic field is applied, the dipoles will tend to align with the applied field, resulting in a net magnetic moment in the direction of the applied field.

• Problems

  • Two oscillating dipole moments (radio antennas) ${\bf d}_1$ and ${\bf d}_2$ are oriented in the vertical direction and are a horizontal distance $L$ apart.They oscillate in phase at the same frequency $\omega$.Consider radiation at an angle $\theta$ with respect to the vertical and in the vertical plane containing the two dipoles.
  • Thus show directly that when $L\ll\ \lambda$, the radiation is the same as from a single oscillating dipole of amplitude $d_1+d_2$.

• Zeeman Effect and Nuclear Spin

  • that can interact with the magnetic moment of the electron.
  • The situtation for the intrinsic magnetic moment of the electron is a bit more subtle.
  • The field of a magnetic dipole is given by
  • This yields a correction to the dipole field called the Fermi contact interaction,
  • A second way to obtain this result is to take the expression for the vector potential of a point magnetic dipole