Shell in a cylindrical capacitor

[fcoulomb]

Homework Statement

There is a capacitor (llenght $L$) made of a conductor (cylinder of radius $R_1$) and a cylindrical surface (radius $R_2$). It is charged with a potential $V_0$, then it is isolated.
(There is vacuum between $R_1$ and $R_2$)

Now we insert a cylindrical conducting shell of thickness $d$, and inside radius $R_3$, as in the picture below.1) Find the capacitance before and after the insertion of the shell. Find the value of $d$ such that $C_{final}=2 C_{initial}$ .

The Attempt at a Solution

[/B]
My question is: after the shell is inserted, there is electrostatic induction between the shell and the $R_1$ cylinder, so i can see the problem as two capacitors in series, BUT the total final capacitance would be always less than the initial.

So how I can start?

 

[kuruman]

Homework Statement

There is a capacitor (llenght $L$) made of a conductor (cylinder of radius $R_1$) and a cylindrical surface (radius $R_2$). It is charged with a potential $V_0$, then it is isolated.
(There is vacuum between $R_1$ and $R_2$)

Now we insert a cylindrical conducting shell of thickness $d$, and inside radius $R_3$, as in the picture below.1) Find the capacitance before and after the insertion of the shell. Find the value of $d$ such that $C_{final}=2 C_{initial}$ .

The Attempt at a Solution

[/B]
My question is: after the shell is inserted, there is electrostatic induction between the shell and the $R_1$ cylinder, so i can see the problem as two capacitors in series, BUT the total final capacitance would be always less than the initial.

So how I can start?

You start by showing some work. Write down the capacitance before the insertion and the capacitances of the two series capacitors after the insertion. Add them as capacitors in series and see if you get a value that is less than the initial. Maybe you won't.