Question

explain Gauss Theorem in Electio
statics Deduce The Expresion for
Electric Intensity at a point near an uniformly Charige sheet?​

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

=  

ϵ  

0

​  

 

q  

in

​  

 

​  

 

E(2πrl)=λl/ϵ  

0

​  

 

E=  

2πrϵ  

0

​  

 

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=  

2πrϵ  

0

​  

 

λ

​