com www.GOALias.blogspot.com

www.GOALias.blogspot.comPhysicsIn an external electric field, thepositive and negative charges of a nonpolarmolecule are displaced in oppositedirections. The displacement stops whenthe external force on the constituentcharges of the molecule is balanced bythe restoring force (due to internal fieldsin the molecule). The non-polar moleculethus develops an induced dipole moment.The dielectric is said to be polarised bythe external field. We consider only thesimple situation when the induced dipolemoment is in the direction of the field andis proportional to the field strength.(Substances for which this assumptionis true are called linear isotropicdielectrics.) The induced dipole momentsof different molecules add up giving a netdipole moment of the dielectric in thepresence of the external field.A dielectric with polar molecules alsodevelops a net dipole moment in anexternal field, but for a different reason.FIGURE 2.22 A dielectric develops a net dipole In the absence of any external field, themoment in an external electric field. (a) Non-polardifferent permanent dipoles are orientedmolecules, (b) Polar molecules.randomly due to thermal agitation; sothe total dipole moment is zero. Whenan external field is applied, the individual dipole moments tend to alignwith the field. When summed over all the molecules, there is then a netdipole moment in the direction of the external field, i.e., the dielectric ispolarised. The extent of polarisation depends on the relative strength oftwo mutually opposite factors: the dipole potential energy in the externalfield tending to align the dipoles with the field and thermal energy tendingto disrupt the alignment. There may be, in addition, the ‘induced dipolemoment’ effect as for non-polar molecules, but generally the alignmenteffect is more important for polar molecules.Thus in either case, whether polar or non-polar, a dielectric developsa net dipole moment in the presence of an external field. The dipolemoment per unit volume is called polarisation and is denoted by P. Forlinear isotropic dielectrics,P = χ eE (2.37)where χ eis a constant characteristic of the dielectric and is known as theelectric susceptibility of the dielectric medium.It is possible to relate χ eto the molecular properties of the substance,but we shall not pursue that here.The question is: how does the polarised dielectric modify the originalexternal field inside it? Let us consider, for simplicity, a rectangulardielectric slab placed in a uniform external field E720parallel to two of itsfaces. The field causes a uniform polarisation P of the dielectric. Thus