Question

State Gauss Law.Use this law to derive an expression for electric field due to infinite line charge​

Answer 1

Answer:

Explanation:

The Gauss law states that electric flux passing through any closed surface is equal to the charge enclosed by that surface divided by permittivity of vacuum.

By symmetry, the magnitude of the electric field will be the same at all points on the curved surface of the cylinder and directed radially outward. E

and ds

are along the same direction.

Now here we have the two surfaces, one curved and other the plane caps,

First, the flux through the curved surface,

∮E

⋅ds

=ϵ0​qin​​

E(2πrl)=λl/ϵ0​

E=2πrϵ0​λ​

Now due to the plane caps,

The angle between E

and ds

is 90,

so the flux through that part is zero

so, Total flux through the closed surface is,

E=2πrϵ0​λ​

Answer 2

Answer:

Gauss Theorem: The net outward electric flux through a closed surface is equal to 1/ε0 times the net charge enclosed within the surface i.e., Let electric charge be uniformly distributed over the surface of a thin, non-conducting infinite sheet. Let the surface charge density (i.e., charge per unit surface area) be s.