Question

10. State Gauss law for electrostatics. Verlinder is lying with a pas
to uniform electric field E. What is the total flux through the
with cross-section Sand length L​

Answer 1

Answer:

Correct Question: State Gauss law for electrostatics. A cylinder is lying with axis parallel to uniform electric field E. What is total flux through the cylinder with area of cross section S and length L.

Gauss Law:

Gauss law states that the total electric field entering a closed surface of some cross sectional area is equivalent to the total amount of charge 'q' enclosed by the surface divided by ∈₀.

Mathematically it is given as:

⇒ ∫ E.dS = q ( enclosed ) / ∈₀

Here, E is the electric field and S is the cross sectional area.

Coming to the other part of your question.

Flux generally denoted by Ф is nothing but ∫ E.dS which is q/∈₀.

Therefore let us break the cylinder into three cases.

Case 1: Flux entering the Cylinder through one face

Case 2: Flux moving inside the Cylinder

Case 3: Flux exiting the cylinder

According to Gauss law, the total flux entering must not be equal to total flux exiting the surface. If both are same, then the total flux is zero.

But according to our cases, Case 1 and Case 3 receive and emit same amount of flux, i.e. incoming flux is equal to outgoing flux. Therefore they cancel out each other.

In between the cylinder, the area vector and surface would be perpendicular due to which Cos A becomes zero. Hence Flux through centre or surface of cylinder is also zero.

Hence net flux passing through a cylinder of cross section S and length L is zero.