7/17/2019 Gauss Law Strategies

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Problem Solving Strategies for Symmetrical Charge Distributions

Gauss’ Law:0ε 

encl  E 

q Ad  E ∫    =•=Φ

System Infinite line of charge Infinite plane of chargeUniformly charged

solid sphere

Figure

Ientify the symmetry Cylinrical Planar S!herical

Determine the irection of E

Divie the s!ace into ifferent

regionsr " 0  z " 0 an z # 0 r $ a an r % a

Choose Gaussian surface

Coa&ial cyliner 

Gaussian !illbo&

Concentric s!here

Calculate electric flu& ( )rl  E  E    π  '=Φ   EA EA EA E    '=+=Φ   ()*   'r  E  E    π  =Φ

Calculate enclose charge

encl q

  l qencl    λ =   Aqencl    σ =

=encl q  Q

ar Q   (+*   ,

ar ar 

≥

≤

-!!ly Gauss’s law:

0ε encl q=Φ

to fin  E   r  E 

0'πε 

λ =

0'ε 

σ = E  = E   

'

0

,

0

)

)

r 

Q

a

Qr 

πε 

πε  

ar 

ar 

≥

≤

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