# Force between cylindrical capacitors

1. Apr 10, 2013

### unscientific

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

I'm not sure what is being varied here, radial separation between capacitors x = (b-a) or whether the capacitors can slide up and down so as to change the length L of the capacitor..

2. Apr 12, 2013

### unscientific

bumpp

3. Apr 12, 2013

### TSny

Since the question states that the inner cylinder is partially withdrawn along the common axis, I think it's L that is varied.

4. Apr 15, 2013

### unscientific

OK, so for constant Q, the force is (1/2)Qo(∂V/∂L), and constant V, the force is (0.5)V^2 (∂C/∂L):

Last edited: Apr 15, 2013
5. Apr 15, 2013

### TSny

How are you defining x? Is it the amount by which the inner conductor is withdrawn or the amount by which the inner conductor is still inside the outer conductor? Or does x represent something else?

How would you write C in terms of x?

6. Apr 15, 2013

### Saitama

Won't it be much better to use the equation $U=\frac{Q^2}{2C}$ and calculate the force when the charge is constant?

7. Apr 15, 2013

### unscientific

Sorry i meant L instead of x.

8. Apr 15, 2013

### unscientific

The C is in the denominator, which gives a C-2(∂C/∂L) term