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superfx

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## Homework Statement

A hollow sphere of gold floats in a large lake of oil of dielectric constant [tex]\kappa=3.3.[/tex] The sphere is half immersed in the oil, and has a total charge of [tex]2.2*10^-6[/tex] Coulombs. What fraction of this electric charge on the sphere is above the oil surface?

## Homework Equations

## The Attempt at a Solution

I'd like to solve this problem in a simple way, without explicitly treating bound and free charges, etc. My line of reasoning is the following: the electric field inside a dielectric is reduced by a factor of [tex]\kappa=3.3[/tex], i.e. [tex]E=E_0/\kappa.[/tex] The sphere is conducting, so the E field inside must be zero-- therefore the charges on the outside must arrange themselves to meet this requirement. The dielectric reduces the field, so I'd expect there to be more free charge on the bottom, in proportion to the dielectric constant. So:

[tex]Q_{top}=\frac{Q_{bottom}}{\kappa}[/tex]

[tex]\frac{Q_{top}}{Q_{total}}=\frac{1}{1+\kappa}[/tex]

Can anyone tell me if my answer is correct or not, and in either case how to reason it through more rigorously? Thanks in advance for your help.