Electric flux, Gauss’s law
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04/22/23 Lecture IV 1
Physics 122
Electric flux, Gauss’s law
Carl Friedrich Gauss
04/22/23 Lecture IV 2
Concepts
• Primary concepts:– Electric flux
04/22/23 Lecture IV 3
Laws
• Gauss’s law
04/22/23 Lecture IV 4
Definition of electric flux
• Flux means flow• Nothing is actually flowing • Other than that thinking of flow really helps to
understand the flux
04/22/23 Lecture IV 5
Electric flux• If electric field is rain – electric
flux is the amount of water in a bucket accumulated per unit of time:
• Only component of the field perpendicular to the area A contributes to the flux
cosEAAE
04/22/23 Lecture IV 6
Electric flux• Alternatively we
can define a vector A, which equals to the area A and is directed perpendicularly to the area
cosEAAE
Flux is proportional to the number of field lines going through the surface
04/22/23 Lecture IV 7
Compare fluxes
Which flux is larger?1). 2).
1 2
04/22/23 Lecture IV 8
Compare fluxes
Which flux is larger?1). 2).
1 2
04/22/23 Lecture IV 9
Compare fluxes
Which flux is larger?1). 2).
1 2
04/22/23 Lecture IV 10
Compare fluxes
Which flux is larger?1). 2).
1 2
04/22/23 Lecture IV 11
Compare fluxes
Which flux is larger?1). 2).
1 2
04/22/23 Lecture IV 12
Compare fluxes
Which flux is larger?1). 2).
1 2
04/22/23 Lecture IV 13
Non-uniform field, irregular surface
• Closed surface
• Influx <0• Outflux>0
Don’t worry, we’ll only deal with simple surfacesComplex surfaces can be handled using numeric integration by a computer.
04/22/23 Lecture IV 14
Why do we need flux?
• Gauss’s law:
04/22/23 Lecture IV 15
Gauss Coulomb • Calculate E of point like (+) charge Q• Consider sphere radius r centered at
the charge• Spherical symmetry: E is the same
everywhere on the sphere, perpendicular to the sphere
04/22/23 Lecture IV 16
Sinks and sources• What goes in – goes out
• unless • there is a source (positive charge)
• or a sink (negative charge)
+
-
04/22/23 Lecture IV 17
What’s the flux?
04/22/23 Lecture IV 18
Respect the symmetry• Find electric field for the following configurations:• Uniformly charged sphere. Charge Q, radius R.
• Long uniform line of charge. Charge per unit length
• Infinite plane of charge. Charge per unit of area
04/22/23 Lecture IV 19
Field near conductor• Infinite plane of charge. Charge per unit of area • Field inside conductoris zero, outside perpendicularto the surface.
04/22/23 Lecture IV 20
Respect the symmetry• Find electric field for the following configurations:• Uniformly charged sphere. Charge Q, radius R.
• Long uniform line of charge. Charge per unit length
• Infinite plane of charge. Charge per unit of area
04/22/23 Lecture IV 21
Two parallel plates
• Infinite plates• One positive, one negative,• Same charge density
02
E
+ -
02
E
0
EEE
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