Capacitor partially dipped in water

[rohith291991]

Homework Statement

A parallel plate capacitor is dipped in a liquid of relative permittivity k horizontally, so that the upper plate remains outside. A source of emf V volt is used to charge the capacitor through a key K. The key K is first closed and then opened. The ratio of respective heights of the level of the liquid from the lower plate is...

Homework Equations

Adgh=F...for equilibrium...

The Attempt at a Solution

i got the first height as h=(((K^2)-1)q^2)/(2(A^2)(K^2)epsilon0dg)

where q is the charge on the capacitor, A is the area of each plate, d is the density...

now my doubt is how to find the force acting on the water in the second case... won't it be the same as the first case?...why should the height change at all?

i saw the solution and it goes like this.. First the potential energy as a function of h was found and the negative of its derivative wrt h gave the force...but why does the energy vary??/ in fact it was given that the energy in the second case is less than in the first case...y is this so?? how is the energy lost??

 

[rohith291991]

please someone help me out...

 

[dynamicsolo]

A parallel plate capacitor is dipped in a liquid of relative permittivity k horizontally, so that the upper plate remains outside. A source of emf V volt is used to charge the capacitor through a key K. The key K is first closed and then opened. The ratio of respective heights of the level of the liquid from the lower plate is...

I think no one has dealt with this problem because it is unclear what the question is. What ratio is being taken here? Is it the ratio of the heights of the liquid between the plates before and after the capacitor has been charged? Is the liquid confined in any way? It reads as if either you omitted some details or the problem isn't well-defined.

 

[rohith291991]

no the capacitor is charged and the key remains closed...let the height of the water be h1...then the key is opened(the capacitor is no longer connected in the circuit)...let the height now be h2... the ratio h2/h1 is asked... i guess this is quitw clear...my doubt is y wud the heights change at all??

 

[rohith291991]

also i don't know what u mean by confined...there is a liquid surface that's all...it doesn't matter whether its the surface of a sea or water in a cup...i don't understand y it shud matter...the question seems to be clear enough...