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physics 2212 exam 2 material
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there is a group of geometric transformations that do not cause any physical change
if you can translate, rotate, or reflect a charge of set of charges and no change is observed, then it is symmetric
when can we say that a charge distribution is symmetric?
the symmetry of the electric field must match the symmetry of the charge distribution
a symmetrical charge distribution is required for the application of gauss' law
If there is no symmetry in E, we cannot easily integrate the left hand side of the gauss law integral, and thus Gauss' Law can't help us.
So basically, it is applied in cases where the Electric field is somehow constant so that it can be pulled out of the integration.
why do we care if charge distribution is symmetric?
planar symmetry
cylindrical symmetry
spherical symmetry
three fundamental symmetries
a closed, mathematical surface around a charge
what is a gaussian surface?
when it matches the shape of the field
when is a gaussian surface most useful?
Gauss' law is a powerful tool for the calculation of electric fields when they originate from charge distributions of sufficient symmetry to apply it.
how is gauss' law useful?
field flows out.
outward flux.
a gaussian surface surrounds a positive point charge. Does the electric field "flow" in or out of the gaussian surface? is the flux inward or outward?
field flows in.
inward flux.
a gaussian surface surrounds a negative point charge. Does the electric field "flow" in or out of the gaussian surface? is the flux inward or outward?
E dot A = EAcostheta
mathematical expression of electric flux (of constant electric field)
∫(surface) E dot dA
we really are only going to be dealing with the cases:
the electric field is tangent everywhere to the surface, so flux=0.
the electric field is everywhere perpendicular to the surface and has the same magnitude E at every point = EA
mathematical expression of electric flux (of nonuniform electric field)
1. choose a gaussian surface made up of pieces that are everywhere tangent to the field or everywhere perpendicular to the electric field
2. use the same method as for a regular surface
how to find the flux through a closed surface?
it allows the electric fields of some continuous distributions of charge to be found much more easily than with coulomb's law.
also gauss's law is valid for moving charges, but coloumb's law is not.
what is the purpose of using Gauss's law?
phi = q/ε₀
what is the flux surrounding a point charge, q?
zero
think about why this is true.
what is the net flux through a closed surface that does not contain any net charge?
add the individual fluxes.
how to find the flux due to multiple charges contained in a gaussian surface?
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