04/22/23 Lecture IV 1

Physics 122

Electric flux, Gauss’s law

Carl Friedrich Gauss

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Concepts

• Primary concepts:– Electric flux

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Laws

• Gauss’s law

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Definition of electric flux

• Flux means flow• Nothing is actually flowing • Other than that thinking of flow really helps to

understand the flux

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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

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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

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Compare fluxes

Which flux is larger?1). 2).

1 2

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Compare fluxes

Which flux is larger?1). 2).

1 2

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Compare fluxes

Which flux is larger?1). 2).

1 2

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Compare fluxes

Which flux is larger?1). 2).

1 2

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Compare fluxes

Which flux is larger?1). 2).

1 2

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Compare fluxes

Which flux is larger?1). 2).

1 2

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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.

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Why do we need flux?

• Gauss’s law:

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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

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Sinks and sources• What goes in – goes out

• unless • there is a source (positive charge)

• or a sink (negative charge)

+

-

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What’s the flux?

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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

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Field near conductor• Infinite plane of charge. Charge per unit of area • Field inside conductoris zero, outside perpendicularto the surface.

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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

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Two parallel plates

• Infinite plates• One positive, one negative,• Same charge density

02

E

+ -

02

E

0

EEE