Electrostatic Fields in Matter

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10 Force on a DielectricIn general, an electric field will exert a torque on a dipole which isnot parallel to the field and a force on a dipole if the two centres ofcharge are at points where the field is different.We will not look at this in detail, although it is covered in Griffiths.However there is an interesting example, which shows how lateralthinking can sometimes get answers out of apparently difficultsituations.Consider the situation shown below.Lx+QA parallel plate capacitor with a slab of dielectric partly insertedbetween the plates. The plates are isolated, so Q, the free charge onthe plates, is constant.Our task is to calculate the force on the dielectric slab. The situationis complex. The field is not constant and hence the polarisationwill also vary with position.The method used is to consider the energy. If the slab moves adistance dx into the capacitor, the energy changes since the capacitancechanges. From conservation of energy we know that the workdone by the force moving the dielectric must be equal to the changein the stored energy.( 1 Q 2 ) (i.e. F dx = ∆ = − 1 Q 2 )dC =(− 1 )2 C 2 C 2 2 V 2 dC (26)14-Q
Take the length of the plates to be L and the distance the dielectricintrudes into the space between the plates to be x. The totalcapacitance is thus:C = ɛ 0A L − xd L+ Kɛ 0A xd L = ɛ 0Ad+ ɛ 0A (K − 1)xd LIf x changes by dx, then the change in C will be:(27)dC = ɛ 0A (K − 1)dx (28)d LCombining equations (26), (27) and (28) gives finally:F = − 1 2 V 2ɛ 0A (K − 1)(29)d LThe expression itself is not particularly important. The interestingpoint is that it is possible to calculate the force in a complex situationin such a simple way.15
Page 3 and 4: 3 Polarisation MechanismsThere are
Page 5 and 6: This leaves a layer of negative cha
Page 7 and 8: The amount of charge in the element
Page 9 and 10: This could all get confusing!Rememb
Page 11 and 12: SolutionSince in this simple geomet
Page 13: 9 Boundary Conditions.What happens
Page 17 and 18: 12 SummaryThe state of a dielectric

Electrostatic Fields in Matter

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