Electrostatic Fields in Matter

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¨¨© ©© ©¨⃗D is convenient because it depends only on the free charge. Youcan calculate ⃗ D in the same way as you calculate ⃗ E, except thatyou only need include the free charge and there will be an ɛ 0 missingsomewhere.The integral form of equation (21) would be:∮⃗D · ⃗da = Q fenc (22)In a dielectric then, we have two equations:∇ · ⃗D = ρ f and ∇ × ⃗ E = 0 (23)ExampleA parallel plate capacitor with plates 5 mm apart is filled withpolythene, which has ɛ r = 2.26. The capacitor is connected to a 9 Vbattery.1. Calculate ⃗ E, ⃗ P , σ b , ⃗ D and σ f in the dielectric.2. Calculate the field due to the free charge and the depolarisingfield.3. What extra information would you need if you wished to calculate⃗p, the atomic dipole moment?¢ ¢ £ £ £ ¢¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡E P D¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥¤¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥¤¦ ¦ ¦ § § § § ¦10
SolutionSince in this simple geometry, all the vector quantities are in thesame direction, we will ignore their vector nature.1.E = V d =P = ɛ 0 (K − 1)E9 V5 mm = 1.8 × 103 Vm −1= 8.85 × 10 −12 (2.26 − 1)1.8 × 10 3= 2.01 × 10 −8 Cm −2σ b = P = 2.01 × 10 −8 Cm −2D = ɛ 0 E + P= 8.85 × 10 −12 × 1.8 × 10 3 + 2.01 × 10 −8= 3.60 × 10 −8 Cm −2σ f = D = 3.60 × 10 −8 Cm −211
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: This could all get confusing!Rememb
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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