Electrostatic Fields in Matter

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5 Parallel Plate Capacitor.A parallel plate capacitor is a useful model for demonstrating someof the basic ideas about dielectrics.The figure shows two parallel conducting plates. A charge Q hasbeen transferred from the bottom plate to the top and the plates arenow isolated.+QAdE-QVFrom Gauss’s law ⃗ E = σ ɛ 0= Q/Aɛ 0(5)V =∫⃗E · ⃗ds = Ed (6)C = Q V = ɛ 0Ad(7)These equations are based on the assumption that the field betweenthe plates is constant, which is reasonable if the plates areclose together.What happens when a dielectric is placed between the plates?The original field, produced by the charges on the plates, pushesthe +ve charges in the dielectric down and -ve charges up. Thedielectric becomes polarised.4
This leaves a layer of negative charge on the top surface of thedielectric and a positive layer at the bottom.The original charge Q, which was placed on the capacitor plates,is referred to as free charge.The charge induced on the dielectric surface is called bound charge.The bound charge generates a new field, in the opposite directionto the original field. This new field is called the depolarisation field.The total field in the dielectric is the sum of the original field (fromthe free charges) and the depolarisation field - it will be smaller thanthe original field.Bound chargesFree chargesDepolarisation fieldOriginal fieldLooking at equations (6) and (7), we see that when a dielectricis placed between charged plates which are not connected, then Qremains constant while V decreases; hence C increases. The factorby which C increases is called the dielectric constant K (or therelative permittivity, ɛ r ).-5
Page 3: 3 Polarisation MechanismsThere are
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 and 14: 9 Boundary Conditions.What happens
Page 15 and 16: Take the length of the plates to be
Page 17 and 18: 12 SummaryThe state of a dielectric

Electrostatic Fields in Matter

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