Paul A Tipler Gene Mosca Physics for Scientists

Gauss’s Law • Electric Flux • Charge Distribution • Relationship between field lines and

Electric Flux • • E varies with density of lines Flux is #lines crossing

Electric Flux (cont. ) • Flux + when leaving a closed surface • Flux

Electric Flux (cont. ) • Notice that there is no charge inside • and,

Case where E is spatially uniform: • f = E·A (E factored out of

Flux through both surfaces is identical 26

Flux and Charge • Amount and sign of a charge can be determined by

(#lines leaving) – (#lines entering) = 0 net charge enclosed is zero 28

net 8 lines leaving = net +q enclosed (with 8 lines per q) 29

• Net Flux not dependent on shape of enclosing surface or any charges

Cylindrical can enclosing part of an “infinite” plane of Q. 33

Plane of Charge cont. Net flux = EA + 0 = 2 EA ==

Gauss’s Law in terms of Permittivity Gauss’s Law Permittivity of a vacuum, Gauss’s Law

Spherical Shell • • cosine = 1 (symmetry) f = EA = Q/eo E

Spherical Shell cont. any closed surface inside shell has Qenc = 0 è EA

Uniform Spherical Volume non-zero values inside same as pt Q outside 40

22 -5 Charge and Field at Conductor Surfaces 43

E on Conductor • at surface E = s/eo • E normal (perpendicular) to

+Point Q inside Shell • shell = neutral conductor • -/+ induced on shell

Summary • E obtained by sum of effect of all charges • charges can

22 -6 Derivation of Gauss’s Law From Coulomb’s Law 48

Slides: 67

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Effect of Symmetry 6

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

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

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

Problems 51