Download Electrostatics in material medium

Electrostatics in material medium
Dielectrics & polarization: are basically insulators which have only bound charges in
contrast to the free charges of a conductor. Here we study electrostatics in presence of
dielectrics – important also for chemistry and biology people to understand.
Polarization: concentration of opposite charges at the ends of a patch of volume or molecule
(large or small) away from equilibrium position – could be due to externally applied electric
~ or inherent assymmetry of charge distribution. In other word, polarization can
field E
be both induced by external magnetic field or permanent. The displacement of charges is
limited by some restoring forces. One of the physical quantities that measure the amount
of polarization is dipole moment.
Dipole moment: In the limit of infinitesimal charge seperation, i.e. distance to the field
point is significantly greater than charge seperation, dipole moment is define as,
p~ = q~s or qd~s.
(1)
~ is proportional to electric field and points to Ê,
Dipole moment induced by external E
~
p~ = αE,
α = atomic polarizability
~ ⇒ pi = αij Ej , αij = polarizability tensor
p~ = [α] E
Polarization is defined as dipole moment per unit volume P~ ≡
(2)
(3)
∆~
p
∆τ .
Permanent dipole moment as a rule are larger by 104 than induced dipole moment. For
instance, for polar molecules HCl, H2 O, N H3 the dipole moments are 1.03 × 10−18 , 1.84 ×
10−18 , 1.43 × 10−18 compared to 0.667 × 10−22 , 24.1 × 10−22 , 1.76 × 10−22 of H, N a, C.
Polarization, induced or permanent, are not necesarily di-polar, they can also be multipolar and have quadru-pole, octo-pole or higher moments.
The dipole moment is determined by the geometry (size, shape and density) of the charge
distribution. The dipole moment of a collection of point charges is
X
(4)
p~ =
qi ~ri0 ,
i
where ~ri0 is defined with respect to some origin. If total charge is zero then the dipole
moment is independent of the choice of origin.
Example 18. Calculate dipole moment of a discrete charge distribution with the charges +2q,
−q and −q at the vertices of an equilateral triangle of side l.
Example 19. Calculate atomic polarizability from a primitive model of an atom, point nucleus of
+q surrounded by uniformly charged spherical cloud of −q [Ref. Griffiths, p161]. For a realistic
model please refer to Am. J. Phys. 54 (1986) 347.
~ field?
Two questions need to be addressed: (i) how a polarized object behaves in external E
(ii) how a polar object itself influences other polar objects? Only dipole moment will be
considered here for these questions.
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