Electric field due to

a uniformly charged

thin spherical shell

 

A) Case 1: 

calculation of electric field outside the shell.

 

1)Consider a thin spherical shell of uniform charged density σ, with radius R,

2) Therefore surface area of the shell is 

Therefore total charge q on the shell is



now we draw a Gaussian closed spherical surface of radius r outside the shell as shown in below.


3)Now the total area of the Gaussian surface of the sphere of radius r is

4)from Gauss’s law, if E is the electric field at a distance r from the centre of the sphere


From  (1.25) putting the value of total charge







Now putting the value of 


from (1.52)

 


 

B) Case 2: 

calculation of electric field inside the shell.

1)Consider a thin spherical shell of radius R, with charge density σ

2) Therefore surface area of the shell is 

Therefore total charge q on the shell is



3) Now draw a gaussian spherical surface of radius r inside the shell.

4) Now as the gaussian surface does not enclose any charge so

q = 0

5) now from Gauss’s law




Since q = 0 as explained above, so


Therefore E = 0

So, electric field inside the shell is zero.