Lecture 27• This week: chapter 27 (Gauss’s Law)

For such fields, calculate using Gauss’s Law

Use symmetry to find geometry of

Concept of Electric Flux in Gauss’s Law

Use Gauss’s Law to understand conductors

Today

Symmetry (unchanged under geom. transformation )

Symmetry II

• must be...

• 3 fundamental symmetries

Concept of Flux

• outward flux (“flow”) of thru’ closed (Gaussian) surface for next positive charge inside

• inward...for...negative...

• no net flux...net charge

E

Concept of Flux II

• match closed surface to symmetry of /charge distributionE

• Analogy:

• Electric Flux (amount of thru’ surface):

• Area vector:

Calculating Electric Flux I

volume of air per second (m3/s) = v A = vA cos !

!e = E A = EA cos !

A = An !

E

Calculating Electric Flux II

!e =!

surfaceE.dA

=!

...EdA

= E

!

...dA = EA

!e =!

i !!e =!

i Ei."!A

#i!

!e =!

surfaceE.dA

=!

...E cos !dA

= E cos !

!

...dA

= E cos !A

Uniform E,flat surface:

Calculating Electric Flux III• Closed surface ( points toward outside: ambiguous for single

surface):

• strategy: divide closed surface into either tangent or perpendicular to

• example: cylindrical charge distribution,

!e =!

E.dA

E

dA

E = E0

!r2/r2

0

"r (r in xy-plane)

!wall = EAwall

!e =!

E.dA

= !top + !bottom + !wall

= 0 + 0 + EAwall

= EAwall

="

E0R2

r20

#(2!RL)