A spherical conducting sphere of inner radius R1 and outer radius R2 has a charge Q.A charge q is placed at the centre of the shell.What is the surface charged density on the(1)inner surface
(2)outer surface of the shell?
 
What is the expression for the electric field at a point to x>R2 from the centre of the shell?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Asked by Rajeev | 12th May, 2015, 03:28: PM

Expert Answer:

The total charge enclosed for the inner sphere is 'q'.
 
Hence, the surface charge density for the inner sphere is begin mathsize 14px style straight sigma subscript inner equals fraction numerator straight q over denominator 4 πR subscript 1 superscript 2 end fraction end style
 
The total charge enclosed for the outer sphere is 'Q+q'.
 
Hence, the surface charge density for the outer sphere is begin mathsize 14px style straight sigma subscript inner equals fraction numerator straight q over denominator 4 πR subscript 1 superscript 2 end fraction end style
 
The electric field at a point at a distance x from the sphere is given by Gauss' law 
 
by imagining a sphere of radius x.
 
begin mathsize 14px style straight E cross times 4 πx squared equals straight Q subscript enclosed over straight epsilon subscript 0 therefore straight E equals fraction numerator straight Q plus straight q over denominator 4 πε subscript 0 straight x squared end fraction end style

Answered by Romal Bhansali | 12th May, 2015, 04:14: PM