{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lectures_Lect04

# Lectures_Lect04 - Physics 212 Lecture 4 Slide Physics 212...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 212 Lecture 4, Slide Physics 212 Lecture 4, Slide 1 Physics 212 Physics 212 Lecture 4 Lecture 4 Gauss’ Law Gauss’ Law Physics 212 Lecture 4, Slide Physics 212 Lecture 4, Slide 2 Gauss’ Law But in cases with symmetry (spheres, cylinders, etc.) we can find a closed surface where 19 In general, the integral to calculate flux is difficult. enclosed closed surface Q E d A E d A ε = = r r v v ￑ E d A r r enclosed Q E d A E d A E A ε = = = r v enclosed Q E A ε = is constant everywhere on the surface. For such cases, Flux: Flux: E field from an infinite line of charge with charge density E field from an infinite line of charge with charge density λ λ Example Example By symmetry, E field points By symmetry, E field points radially radially outward outward ( for positive ( for positive λ λ ) E r E r d A r d A r ( 29 2 sides E d A E r rL π = r r r r L L C ho o s e c ylinde r o f ra dius r, le ng th L, c e nte re d o n the line o f c ha rg e . and and ends E d A = r r ( 29 2 enclosed Q L E d A E r rL λ π ε ε = = = r r ￑ s s o o ( 29 2 E r r λ π ε = Phys ic s 212 Le c ture 4, S lide Phys ic s 212 Le c ture 4, S lide 4 Exam ple s with S ym m e try ε = enc Q E A Spherical Cylindrical Planar 2 4 π = A r 2 4 π ε = enc Q E r 2 π = A rL 2 λ π ε = E r 2 2 π = A r 2 σ ε = E 21 ∫ = ⋅ o enc Q A d E ε r ￑ Phys ic s 212 Le c ture 4, S lide Phys ic s 212 Le c ture 4, S lide 5 C he c kpo int 4 27 In which case is E at point P the biggest? A) A B) B C) the same Re c a ll tha t fo r a n infinite pla ne with c ha rg e de ns ity σ (C o ul/m 2), E = E = σ /2 ε Phys ic s 212 Le c ture 4, S lide Phys ic s 212 Le c ture 4, S lide 6 +- + Case A Case B + Superposition !...
View Full Document

{[ snackBarMessage ]}