Electric flux: is defined as total number of electric field lines passing from any area, denoted by ΦE or f mathematically it is defined as integral of E and dS
Φ = ∫E.dS with units of Newton meter2/Coulomb
Remember area vector S is perpendicular to the surface of area under consideration.
Gauss Law: states that surface integral of electric field produced by any source over any closed surface S enclosing a volume V is 1/ε0 times total charge contained inside surface.
Electric flux is proportional to the number of electric field lines penetrating some surface.
It is to note that electric charges outside Gaussian surface do not contribute to electric flux.
1. The value of the electric field can be argued by symmetry to be constant over
the surface.
2. The dot product in E.dS can be expressed as a simple algebraic product E dA whenever because E and dA are parallel.
3. The dot product in E.dS is zero whenever E and dA are perpendicular.
4. The field can be argued to be zero over the surface. OR constant
All four of these conditions are used in examples throughout the remainder of
this chapter.
READ THE CONCEPTS IN DETAIL BEFORE DERIVATION
WE have to to certain standard derivations on the above basis.
- Electric field due to a point charge, taking Gaussian surface as sphere.
- Coulomb law on the above basis
- Electric field due to a linear charge, taking Gaussian surface as cylinder
- Electric field due to a charged sheet, taking Gaussian surface as cylinder or cuboid.
- Electric field due to a charged shell, taking Gaussian surface as sphere in and out
- Electric field due to a conducting sphere, taking Gaussian surface as sphere in and out
- Electric field due to a uniformly charged sphere (Obviously it is non conducting), taking Gaussian surface as sphere.
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