Physics · Ch 8 — Electrostatics

Dielectrics and Electric Polarisation

8.8

Dielectrics and Electric Polarisation

DIELECTRICS are insulating materials -- familiar examples include glass, wax, water, wood, mica, rubber, stone and plastic -- that can be used to STORE electrical energy, precisely because when placed inside an external electric field, the positive and negative charges within each of their molecules shift slightly apart, so the material as a whole develops a net dipole moment. This shifting-apart process is called POLARISATION, and any material capable of it is, by definition, a dielectric.

Every individual atom consists of a positively charged nucleus surrounded by a cloud of negatively charged electrons -- each of these two oppositely-charged regions has its own distinct CENTRE of charge (formally, the centre of mass of that particular charge distribution): a centre of positive charge (essentially the nucleus itself) and a separate centre of negative charge (the electron cloud's own centroid). Whether or not these two centres coincide, in a molecule's normal, field-free state, is exactly what splits all dielectric materials into two broad classes.

POLAR molecules -- such as HCl, water, ammonia, sulphur dioxide and sodium chloride -- have an inherently ASYMMETRIC shape, so their positive and negative charge centres do NOT coincide even with no external field present at all; each such molecule therefore already possesses a small, PERMANENT dipole moment of its own, typically of order $10^{-30}$ C m. Water is a particularly striking example: its two O-H bonds meet at an angle of about $105^\circ$ rather than sitting in a straight line, giving it an unusually large permanent dipole moment of $6.1\times10^{-30}$ C m among common polar substances. NON-POLAR molecules -- such as $H_2$ , $Cl_2$ , $CO_2$ and $CH_4$ -- are, by contrast, symmetric in shape, so their positive and negative centres coincide EXACTLY at the same point in the molecule's normal state, giving zero net dipole moment. An external field can still act on a non-polar molecule, however: it pulls the positive centre slightly along the field direction and pushes the negative centre the opposite way, distorting the molecule into a tiny INDUCED dipole -- this displacement continues only until the pull of the external field is exactly balanced by the newly-induced dipole's own restoring internal field, at which point the induced separation stabilises. A POLAR molecule's permanent dipoles, meanwhile, start out randomly oriented by ordinary thermal agitation when no field is present, so their individual dipole moments cancel out to a net zero for the material as a whole -- but an applied external field tends to ALIGN these already-existing permanent dipoles with itself (though never perfectly, since thermal agitation continues to fight against full alignment), again giving the bulk material a net dipole moment pointing along the field. So BOTH polar and non-polar dielectrics end up developing a net dipole moment once a field is switched on, even though the underlying mechanism differs -- alignment of pre-existing dipoles for polar materials, versus creation of entirely new induced dipoles for non-polar ones.

The dipole moment PER UNIT VOLUME of a polarised dielectric is called its POLARISATION, denoted $\vec{P}$ . For a LINEAR, ISOTROPIC dielectric (one whose response is simply proportional to the applied field and identical in every direction), $\vec{P}=\chi_e\vec{E}$ , where $\chi_e$ is a material-specific constant called the ELECTRIC SUSCEPTIBILITY, describing how readily that particular dielectric polarises under a given field; for vacuum itself, $\chi_e=0$ , since there is nothing there to polarise at all. …

Figure 8.18Fig. 8.18 (a)-(c): A polar molecule, and the structures of HCl and H2O