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I have a non conducting sphere with a charge ρ=A/r per uni vollume A is constant. suppose there is a cavity in the centre and within a particle of charge q. i want to find the E inside the sphere in respect with r.

for radius equal of the cavity i get ##E=kq/r^2## for r bigger than the radius of the sphere ##E=k(Q+q)/r^2## now only one case left

if r is bigger than the radius of the cavity and smaller than the radius of the sphere.

##E4πr^2=\frac{q+ρV}{ε_0} ##

where ρ is the density per unit vollume and V is the vollume

is my enclosed Q right? and my V is 4π(r^3-a^3) where a^3 is the small radius.

## Homework Equations

## The Attempt at a Solution

for radius equal of the cavity i get ##E=kq/r^2## for r bigger than the radius of the sphere ##E=k(Q+q)/r^2## now only one case left

if r is bigger than the radius of the cavity and smaller than the radius of the sphere.

##E4πr^2=\frac{q+ρV}{ε_0} ##

where ρ is the density per unit vollume and V is the vollume

is my enclosed Q right? and my V is 4π(r^3-a^3) where a^3 is the small radius.

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