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## Homework Statement

Consider a conducting sphere with radius ##R## connected to a voltage source of ##V_0## volts. If the sphere is then covered by a dielectric spherical layer of radius ##9R## calculated the relative permitivitty ##\varepsilon_0## needed so that the field in the empty zone (##r<9R##) is 1.5 times stronger than without the dielectric shield.

## Homework Equations

To find the field without dielectric:

##\iiint E\cdot dS = \frac{Q_0}{\varepsilon_0}##

With dielectric:

##\iint D\cdot dS= \frac{Q_0+Q_{bound}}{/varepsilon_0}##

## The Attempt at a Solution

So I tried to calculate ##Q_0## first, I got as a hint that I should calculate it in terms of ##V_0##, then I should calculate ##Q_0+Q_{bound}## considering voltage remains constant. That's the part I'm stuck, I don't know how to calculate charge in terms of voltage. Besides I think some of my equations are a bit off.