Question

state gauss theorum and apply it to charged electric shell

Answer 1

Gauss' theorem states that the total electric flux through any closed surface is proportional to the total electric charge inside the surface.

a) As per Gauss’ law, the electric field intensity at point P on an infinitely long straight charged line is:  

Here we have  

λ = linear charge density  

ε0 = electrical permittivity of free space  

r = radius  

ȓ = unit vector in the direction of radius.

b) For a uniform charged infinite plane sheet having uniform surface charge density σ, point P situated at a perpendicular distance r from the given plane, then the electric filed intensity as per the Gauss’ law is:

Here we have  

σ = Surface charge density  

ε0 = electrical permittivity of free space

c) For a spherical shell having surface charge density σ and radius R, the electric field resulting from such a spherical shell is radial and hence electric field intensity is calculated for a point lying inside and outside the spherical shell.  

Point lying inside the shell:  

Here point is lying inside the shell and having radius r smaller then the spherical shell radius R. So, as per the Gauss’ law, the electric field intensity is zero due to charge enclosed by such a surface is zero as the radius is concentric with the shell.  

Point lying outside the shell:  

Here point is lying outside the shell and having radius r greater then the spherical shell radius R. So, as per the Gauss’ law, the electric field intensity is,