24.4 Dielectrics
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Dielectrics Experiment: Place dielectrics between plates of capacitor at Q=const condition Observation: potential difference decreases to smaller value with dielectric material relative to air Without dielectric: πΆ0 = With dielectric: πΆ= π π0 π π Κ: = π = ππππ π‘ πΆ π0 = πΆ0 π because V<V0 C>C0 K>1: relative dielectric constant What happens with the E-field in the presence of dielectric material πΈ = πππππ πΈ0 π0 πΈ0 We know V<V0 E<E0 specifically πΈ= Κ= = Κ π πΈ d Recall: πΈ = ππππ‘ π0 ππππ‘ reduced with dielectric material The surface charge (density) σ on conducting plates does not change but induced charge σi of opposite sign π πΈ0 = π0 and πΈ = π − ππ π0 π πΎπ0 1 ππ = π(1 − ) πΎ πΈ= π = πΎπ0 Definition of the permittivity π΄ 1 πΆ = π π and π’ = 2 ππΈ 2 DIELECTRICS +Q Example: E0 E1 E2 K1 K2 d/2 d/2 V -Q πΈ0 πΈ1 πΈ2 π π = = π0 π0 π΄ πΈ0 π = = πΎ1 π0 π΄πΎ1 πΈ0 π = = πΎ2 π0 π΄πΎ2 π1 = π(1 − 1 ) πΎ1 π2 π π= = 4π π΄ 0 π0 1 = 4 (πΈ2 πΎ2 )2 πΎ + 1 1 ππ 2 π π + πΈ2 2 2 π π π ππ 1 1 = + = ( + ) π0 π΄πΎ1 π0 π΄πΎ2 2 2π0 π΄ πΎ1 πΎ2 V = πΈ1 π π 2π0 π΄πΎ1 πΎ2 πΆ= = = ππ 1 1 π ( + ) π(πΎ1 + πΎ2 ) 2π0 π΄ πΎ1 πΎ2 1 π2 = π(1 − ) πΎ2 1 πΎ1 1 πΎ2 1 π 1 π + πΎ πππ π’ = π΄π = 4π (π΄ )2 2 0 1 πΎ1 1 π + πΎ = 40 (πΈ1 πΎ1 )2 2 1 πΎ1 1 +πΎ 2 24.4 DIELECTRICS Dielectric breakdown or Dielectric strength High Voltage Ground Ground Air Cr2O3 GAUSS’S LAW IN DIELECTRICS Recall: πππππ π0 = πΈ β ππ΄ πΈ≠0 πΈ=0 Dielectrics Conductor πππππ = π − ππ π΄ πΈ β ππ΄ = πΈπ΄ πΈπ΄ = π −ππ π − ππ π΄ π0 1 ππ = π(1 − ) πΎ πΈπ΄ = ππ΄ πΎπ0 πππππ−ππππ = π0 A A A πΎπΈ β ππ΄ GAUSS’S LAW IN DIELECTRICS πππππ−ππππ = π0 Example: K E1 ra r rb E2 π= ππ ππ π= ππ ππ π1 (ππ − ππ ) πΈ1 ππ = 2π0 πΎπππ ππ πΈ2 ππ = π2 (ππ − ππ ) 2π0 πππ ππ πΎπΈ β ππ΄ π = π0 πΎπΈ β ππ΄ = πΎπΈ1 2ππ 2 + πΈ2 2ππ 2 π2 π1 π0 π0 π1 πΈ1 = 2π0 πΎππ 2 π2 πΈ2 = 2π0 ππ 2 2π0 πΎπππ ππ π π1 = (ππ − ππ ) π2 = 2π0 πππ ππ π (ππ − ππ ) 2π0 πππ ππ π π = π1 + π2 = (πΎ + 1) ππ − ππ πΆ= π 2π0 πππ ππ (πΎ + 1) = π (ππ − ππ ) MOLECULAR MODEL OF INDUCED CHARGE CLICKER QUESTION A conductor is an extreme case of a dielectric, since if an electric field is applied to a conductor, charges are free to move within the conductor to set up “induced charges”. What is the dielectric constant of a perfect conductor? A. K = 0 B. K = ο₯ C. A value depends on the material of the conductor E E0 ο½ ο³0 οο³i ο³0 ο½ 1 K 8
