Question

Deive the expression
electric field
due to
an
infinity line
chave:​

Answer 1

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​