Topic 3: Gauss's Law Flashcards
What is flux?
It is helpful to imagine electric flux radiating from a point positive charge, hence the charge is a source of electric flux.
- Between the two point charges, there are lines of electric field, E, and we can imagine these lines replaced by tubes of electric flux(Y) Coulombs.
The electric flux density?
The electric flux density D can be given by Y/A, where A is the cross-sectional area of the flux density.
The equation for electric flux density(D)
For this to be true the electric flux must pass normally through, that is at right angles to, the cross-sectional surface. Hence,
Y = DA
Where A is the perpendicular cross-sectional area and A is the flux density.
Illustration of electric flux?
The relationship between electric flux density and electric field?
Electric flux density(D) is directly proportional to electric field(E)
The relationship between the electric field and density through surface integrals?
where D.ds is the vector dot product
Calculating the vector dot product D.ds?
D.ds = |D|.|ds|.cosØ
The surface integral of D with respect to ds, where D.ds is the total electrical flux crossing the surface S
The total electric flux connecting two charges can be given by?
Gauss’ Law
The electric flux passing through any closed surface is equal to the total charge enclosed.
Electric flux density in a sphere?
If S is a sphere, then by symmetry D is the same over the surface
The equation for Q, D and E when dealing with a sphere?
General equation for Electric flux density in air or vacuum?
D = e0E
General equation for electric flux density in linear isotropic materials?
D = e0erE
The E field and D for a cylinder?
The E field can be found through Gauss Law
The surface:
The E field and Gaussian surface can be calculated:
The electric field produced by a charge Q which is uniformly distributed over the surface of a thin spherical shell of radius a.
