Question

derive gauss theorem in a easy method plzzzz fast

Answer 1

it state that the total flux through a closed surface is 1/€ times the net charge (q) enclosed by the closed surface .
mathematically
E.ds=q/€
where € is permitivity of medium .
1) if total enclosed charge zero i.e.q=0
then total electric flux =0

2)if a closed body , not enclosing any charge is placed in an electric field (either uniform or non-uniiform) then total flux linked with it will be zero.

Answer 2

Answer:

Explanation:

According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.

∮E⃗ .d⃗ s=1∈0q .

According to Gauss Law,

Φ = → E.d → A

Φ = Φcurved + Φtop + Φbottom

Φ = → E . d → A = ∫E . dA cos 0 + ∫E . dA cos 90° + ∫E . dA cos 90°

Φ = ∫E . dA × 1

Due to radial symmetry, the curved surface is equidistant from the line of charge and the electric field in the surface has a constant magnitude throughout.

Φ = ∫E . dA = E ∫dA = E . 2πrl

The net charge enclosed by the surface is:

qnet = λ.l

Using Gauss theorem,

Φ = E × 2πrl = qnet/ε0 = λl/ε0

E × 2πrl = λl/ε0

E = λ/2πrε0