The homogeneous electric field

In case of a homogeneous external electric field, the contribution to comes from the first term in eq. (12.10)  

On the other hand, in the case of a weak electric field we certainly may write the Taylor expansion  

Linear and non-linear responses to a homogeneous electric fieid 

The meaning of the formula for fig is clear in addition to the permanent dipole moment fiQ of the isolated molecule, we have its modification, i.e. an induced dipole moment, which consists of the linear part in the field J g, agg Egr) and of 

we obtain higher-order dipole hyperpolarizabilities (- .), which will contribute to the characteristics of the way the molecule is polarized when subject to a weak electric field. 

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Figure 3. Illustration of the cross-beam machine. N is the nozzle source for the molecular beam, C is the buffer chamber with a beam chopper (not shown), H is the hexapole electric field quantum state selector, U are the homogeneous electric field plates, Q is an on-axis quadrupole mass filter, O is the fast atom beam source, and Q and C,8o are channeltrons.

Since in the present example the homogeneous electric field affects only the longitudinal velocity, but not the transverse velocity, one has... 

E = (t>/l is the homogeneous electric field between the plates. p is the space charge density. 

The Electric Field as a Perturbation The Homogeneous Electric Field... 

Figure 6.10 The velocity profile, U, and the negative Debye layer charge density profile, in an ideal electroosmotic (EO) flow inside a channel. The EO flow is induced by the external potential difference A0 = Ay, resulting in the homogeneous electric field E. The velocity profile reaches the constant value at a distance of a few times the Debye length from the walls...

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