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How to use Gauss’s Law
Count the lines leaving a surface as +Count the lines entering a surface as –Figures 23-10 and 23-11 on p.696
Gauss’s Law
Relates the electric field on a closed surface to the net charge within the system
For static charges, Gauss’s Law and Coulomb’s Law are EQUIVALENT
Gauss’s Law: The net number of lines leaving any surface enclosing the charges is proportional to the net charge enclosed by the surface
Electric Flux Φ
The mathematical quantity that corresponds to the number of field lines crossing a surface
For a surface perpendicular to the Electric Field, the flux is defined as the product of the magnitude of the field E and the area A:
Φ = EA (units are Nm2/C)
The box may enclose a charge, by placing a test charge and observing F, we know E. It is only necessary to do this at the surface of the shape.
Electric Flux Φ continued
When the area is NOT perpendicular to E, then the following equation is used:
Φ = EAcosθ = EnA
Where En is the component of E that is perpendicular or normal to the surface
Flux
Flux, in this case Electric Flux, is the amount of (electric) field passing through a specified area.
Think of water flowing in a pipe (flux comes from the Latin for “flow”)
The E-field decreases at 1/r2 while the area increases at r2 and that increase and decrease cancel each other out and that is why the size of the surface enclosing Q does not matter.
Electric Flux Φ continued
What if E varies over a surface? (see Fig 23-14 on p.697)
If we take very small areas A that can be considered a plane, we can then sum the fluxes for each area using Calculus
Quantitative Statement of Gauss’s Law
P698The net flux through any surface equals
4πk times the net charge inside the surface
What we can conclude about Ф
1. Ф is proportional to q
2. Whether Ф is inward or outward depends on the q inside the surface
3. A q outside the surface offers zero Ф because Фin = Фout