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## Homework Statement

The electric field produced by a static electric charge P

_{e}(R) at a point R in free space is give by,

E(R) = (R

^{3}+AR

^{2}) R[tex]\hat{}[/tex] , R<a

E(R) = B(a

^{5}+Aa

^{4})R

^{-2 }R[tex]\hat{}[/tex], R>a

Where a, A and B are arbitrary constants and R spherical coordinate system radial vector (R locates the observation point at its tip).

Determine the associated charge distribution P

_{e}(R)

## Homework Equations

## The Attempt at a Solution

By Helmholtz theorem,

E(R) is given by -[tex]\Delta[/tex][tex]\Phi[/tex]

Where,

[tex]\Phi[/tex] = (1/4piε)[tex]\int[/tex](P

_{e}/|R-R'|)dv'

I am not sure how to make use of the R<a and R>a conditions. I am thinking, when its R>a, the volume integral is just r

^{2}sin θ dθ dφ dr

When R<a, the only the radius changes to (a-R)

^{2}?