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## Main Question or Discussion Point

A thick spherical shell (inner radius a, outer radius b) is made of dielectric materials with a "frozen-in"polarization

P(r) =k/r rhat;

where k is a constant and r is the distance from the centre. There is no free charge.

Find the electric field E in all three regions by two different methods:

(a) Locate all the bound charge, and use Gauss’ law to calculate the field E produced.

Im stuck for a<r<b

so using gauss's law for a<r<b ,

I need to find the Q enc= ∫-k/r^2dr (4πr^2) between r and a , k/r^2 comes from usinfg ∇.P=-k/r^2 , which I get to be -4∏(r-a)k ..which is not the answer its -4∏(r)k , which means Qencl is actually=-4∏(a)+4∏(r-a)k, so I have missed the charge at a ..But isnt the integral take into account all the charges from r to a, do I need to an additional -4∏(a)k just at r=a?

can someone explain why?

Thanks :)

P(r) =k/r rhat;

where k is a constant and r is the distance from the centre. There is no free charge.

Find the electric field E in all three regions by two different methods:

(a) Locate all the bound charge, and use Gauss’ law to calculate the field E produced.

Im stuck for a<r<b

so using gauss's law for a<r<b ,

I need to find the Q enc= ∫-k/r^2dr (4πr^2) between r and a , k/r^2 comes from usinfg ∇.P=-k/r^2 , which I get to be -4∏(r-a)k ..which is not the answer its -4∏(r)k , which means Qencl is actually=-4∏(a)+4∏(r-a)k, so I have missed the charge at a ..But isnt the integral take into account all the charges from r to a, do I need to an additional -4∏(a)k just at r=a?

can someone explain why?

Thanks :)