How to Find the Capacitance of an Isolated Ball-Shaped Conductor?

[Shreyas Shree]

Homework Statement

Find the capacitance of an isolated ball-shaped conductor of charge q
of radius Ri surrounded by an adjacent concentric layer of dielectric
with permittivity E and outside radius R2.

Homework Equations

3. The Attempt at a Solution [/B]
I haven't understood the very first line. Otherwise everything else is fine.
From the first line, it says that we take a Gaussian surface between R1 and R2, and hence we have a charge q enclosed and we integrate this from R2 to R1. This is also fine. But my problem lies in the step where we take a Gaussian surface outside the capacitor and we integrate it from infinity to R2. But how is the charge enclosed q, should'nt it be zero?

 

[ehild]

Homework Statement

Find the capacitance of an isolated ball-shaped conductor of charge q
of radius Ri surrounded by an adjacent concentric layer of dielectric
with permittivity E and outside radius R2.

Homework Equations

View attachment 88129
3. The Attempt at a Solution [/B]
I haven't understood the very first line. Otherwise everything else is fine.
From the first line, it says that we take a Gaussian surface between R1 and R2, and hence we have a charge q enclosed and we integrate this from R2 to R1. This is also fine. But my problem lies in the step where we take a Gaussian surface outside the capacitor and we integrate it from infinity to R2. But how is the charge enclosed q, should'nt it be zero?

You integrate with respect to r, he distance from the centre, from R2 to infinity. And you need to consider the charge enclosed by the Gaussian surface of radius r.

 

[Shreyas Shree]

aaaahhh! nice! Thank you very much