Paul A Tipler Gene Mosca Physics for Scientists
- Slides: 67
Paul A. Tipler • Gene Mosca Physics for Scientists and Engineers Fifth Edition Chapter 22: The Electric Field II: Continuous Charge Distributions Copyright © 2004 by W. H. Freeman & Company 1
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Effect of Symmetry 6
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22 -2 Gauss’s Law 20
Gauss’s Law • Electric Flux • Charge Distribution • Relationship between field lines and charge 21
Electric Flux • • E varies with density of lines Flux is #lines crossing a specific area Flux and “Flow” Symbol f Units: N·m 2/C Product of Field and Area Can be + or 22
Electric Flux (cont. ) • Flux + when leaving a closed surface • Flux - when entering a closed surface 23
Electric Flux (cont. ) • Notice that there is no charge inside • and, Net Flux is zero 24
Case where E is spatially uniform: • f = E·A (E factored out of integral) • f = +EA (E parallel to A) • f = -EA (E anti-parallel to A) 25
Flux through both surfaces is identical 26
Flux and Charge • Amount and sign of a charge can be determined by (#lines leaving) – (#lines entering) 27
(#lines leaving) – (#lines entering) = 0 net charge enclosed is zero 28
net 8 lines leaving = net +q enclosed (with 8 lines per q) 29
Flux due to a point Q 30
• Net Flux not dependent on shape of enclosing surface or any charges outside the enclosure • Net Flux does depend on amount of charge inside enclosure 31
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Cylindrical can enclosing part of an “infinite” plane of Q. 33
Plane of Charge cont. Net flux = EA + 0 = 2 EA == 4 pkq E = 4 pkq/2 A = 2 pk(q/A) = 2 pks. 34
Gauss’s Law in terms of Permittivity Gauss’s Law Permittivity of a vacuum, Gauss’s Law 35
Spherical Shell • • cosine = 1 (symmetry) f = EA = Q/eo E = Q/eo. A A = 4 pr 2. 36
Spherical Shell cont. any closed surface inside shell has Qenc = 0 è EA ~ Q = 0 èE=0 37
“Field”: Concept or Reality? 38
Long Line 39
Uniform Spherical Volume non-zero values inside same as pt Q outside 40
22 -4 Discontinuity of En 41
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22 -5 Charge and Field at Conductor Surfaces 43
E on Conductor • at surface E = s/eo • E normal (perpendicular) to surface • E is zero inside (with static charges) 44
+Point Q inside Shell • shell = neutral conductor • -/+ induced on shell • E ~ same as for lone +pt Q. 45
Charge Distribution Field Shape 46
Summary • E obtained by sum of effect of all charges • charges can be point (ch 21) or ‘continuous’ (ch 22) • E can also be obtained by use of Gauss’s Law for E, where concept of E flux is used. 47
22 -6 Derivation of Gauss’s Law From Coulomb’s Law 48
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Problems 51
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