Gauss's Theorem: The net electric flux passing through any closed surface is
times, the total charge q present inside it.
Mathematically, Φ= ε o 1 ⋅q
Proof: Let a charge q be situated at a point O within a closed surface S as shown. Point P is situated on the closed surface at a distance r from O. The intensity of electric field at point P will be
Eˉ=4πεo1⋅r2q .......(1)
Electric flux passing through area ds enclosing point P,
dΦ=E⋅ds
or dΦ=E⋅dscosθ
[where θ is the angle between E and ds]
Flux passing through the whole surface S,
∫∫sdΦ=∫∫sE⋅dscosθ ........(2)
