How does the dielectric affect the charge distribution on a charged sphere?

[Apashanka]

Homework Statement

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Homework Equations

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∫D_{perpendicular}ds=q_{enclosed freecharge}
D=ε₀E+P

The Attempt at a Solution

D₁+D₂=q/2πr²
at a distance r from the centre
How to find D₂ which is at the lower boundary e.g inside the dielectric??

 

[scottdave]

Think about how, if any, would the dielectric change how the charge is on the sphere.