# How an induced electric dipole vibrates with EM field

• I
• Salmone
I thought we discuss Rayleigh scattering, i.e., the scattering of an electromagnetic wave on a neutral "atom". The most simple approximation, assuming a classical non-relativistic harmonic oscillator including radiation reaction in the Landau-Lifshitz approximation of the Lorentz-Abraham-Dirac equation (imho the best one can do within classical theory), you find in Jackson, Classical Electrodynamics.Yes, there is a very simple approximation to the scattering of an electromagnetic wave on a neutral molecule in which radiation reaction is taken into account in the Landau-Lifshitz approximation of the Lorentz-Abraham-Dirac equation. This approximation is called the Jackson theory, and

#### Salmone

If we have an electromagnetic wave like the one in the picture and a molecule which is, in the image, the small black ball with electron cloud being the part with "minus sign" in it, does the molecule with its cloud start to oscillate, once the EM wave hits it, as an induced electric dipole, along the z-axis or along the x-axis? (The two axes are as drawn in the figure).

Delta2
The particle you have shown seems to be an atom. It is electrically neutral so does not respond to electric fields. If we consider a particle with an overall charge, such as an ion or electron, then it will move in the E direction in response to the electric field of the wave. Some molecules have asymmetrical charge distribution on them and these will also respond to the E-field.

Of course a neutral particle consisting of charged particles respond to electromagnetic fields. The standard approximate treatment is the dipole approximation, i.e., the electric field induces a dipole moment.

Lord Jestocost, Delta2, Twigg and 1 other person
If the neutral particle is subjected to a uniform electric field, then by induction we expect one end to become positive and the other negative. But if the field is uniform, these will experience equal forces in opposite directions. So it seems to me that the object will not move.

The object won't move, but that doesn't mean that it doesn't respond to an external electric field. If it had an electric dipole moment before the electric field has been switched on, this dipole moment will be redirected in the direction of the electric field. If it hasn't an own dipole moment, there will be induced one due to the field.

Lord Jestocost, Delta2 and Twigg
Salmone said:
does the molecule with its cloud start to oscillate, once the EM wave hits it, as an induced electric dipole, along the z-axis or along the x-axis?
Given that the E-field points along the positive z-axis, what will be the direction of the electric force experienced by the electrons? As an approximation (and a pretty good one at that), you can ignore the magnetic field.

Hmm guys, a related question but I am not good in chemistry, but with my physics knowledge I think most molecules (organic or anorganic) have net dipole moment (and I don't mean the induced one) because even though the molecule is electrically neutral, I would expect to be a rare coincidence that the charge density ##\rho## is perfectly symmetrically distributed as to eliminate the net dipole moment ##\int\rho (r') (r-r')d^3r'##.

Delta2 said:
Hmm guys, a related question but I am not good in chemistry, but with my physics knowledge I think most molecules (organic or anorganic) have net dipole moment
Yes, molecules can be electrically neutral and have a permanent electric dipole moment. Additionally, a neutral molecule can have an induced dipole moment (given in the limit of small applied fields by its polarizability). You can keep going all the way up the multipole expansion and find all the multipole moments of a molecule, permanent and induced. "Neutral molecule" only means "no monopole".

To reiterate what's been stated above, the idea that a neutral molecule doesn't respond to electric fields is false. I think post #2 meant to say that there is no monopole interaction since there is no net charge. An electric field can induce a force on a neutral molecule, even if that molecule has a weak permanent dipole moment at zero field, provided the electric field has a gradient. This physics is the core principle behind the Stark decelerator. (Sorry I couldn't find a better introductory summary on the topic.) It's not stated in this summary, but some of the most successful Stark decelerators couple to induced dipole moments more strongly than permanent dipoles (example here).

Delta2
Very interesting to learn about the Stark Decelerator, thank you. But for a uniform E-field I think we can say the neutral particle does not move, even though it may have or acquire a dipole.

Delta2
I thought we discuss Rayleigh scattering, i.e., the scattering of an electromagnetic wave on a neutral "atom". The most simple approximation, assuming a classical non-relativistic harmonic oscillator including radiation reaction in the Landau-Lifshitz approximation of the Lorentz-Abraham-Dirac equation (imho the best one can do within classical theory), you find in Jackson, Classical Electrodynamics.

Twigg and Delta2
Twigg said:
Given that the E-field points along the positive z-axis, what will be the direction of the electric force experienced by the electrons? As an approximation (and a pretty good one at that), you can ignore the magnetic field.
I guess along the z-axis so that is the axis along which the dipole will oscillate, right?

Twigg