- #1
Argelium
- 25
- 7
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.