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This sample is taken from Problems of the 6^th International Physics Olympiad (Bucharest, Romania in 1972) problem 3.

Problem 3 (Electricity)
A plane capacitor with rectangular plates is fixed in a vertical position having the lower part in contact with a dielectric liquid (fig. 3.1) Determine the height, h, of the liquid between the plates and explain the phenomenon. The capillarity effects are neglected. It is supposed that the distance between the plates is much smaller than the linear dimensions of the plates.

It is known: the initial intensity of the electric field of the charged capacitor, E, the density ρ, the relative electric permittivity εr of the liquid, and the height H of the plates of the capacitor.
Discussion.

Solution Problem 3

The initial energy on the capacitor is:



H is the height of the plates, l is the width of the capacitor’s plates, and d is the distance between the plates.
When the plates contact the liquid’s surface on the dielectric liquid is exerted a vertical force. The total electric charge remains constant and there is no energy transferred to the system from outside. The increase of the gravitational energy is compensated by the decrease of the electrical energy on the capacitor:



Introducing (3) and (4) in equation (2) it results:



The solution is:



Discussion: Only the positive solution has sense. Taking in account that H is much more grater than h we obtain the final result:



Reposted : Fisikastudycenter.com
Sources/Literatures:
-Problems of the 6^th International Physics Olympiad (Bucharest, 1972) Romulus Pop, Civil Engineering University, Physics Department Bucharest, Romania
-The Olympic home page www.jyu.fi/ipho