IPhO 1972, Теория и експеримент — Задача 3. Problem 3 (Electricity)
Problems of the 6th International Physics Olympiad (Bucharest, 1972) · 10 т.
Romulus Pop, Civil Engineering University, Physics Department, Bucharest, Romania
The sixth IPhO was held in Bucharest and the participants were: Bulgaria, Czechoslovakia, Cuba, France, German Democratic Republic, Hungary, Poland, Romania, and Soviet Union. It was an important event because it was the first time when a non-European country and a western country participated (Cuba), and Sweden sent one observer.
The International Board selected four theoretical problems and an experimental problem. Each theoretical problem was scored from 0 to 10 and the maximum score for the experimental problem was 20. The highest score corresponding to actual marking system was 47,5 points. Each team consisted in six students. Four students obtained the first prize, seven students obtained the second prize, ten students obtained the third prize, thirteen students had got honorable mentions, and two special prizes were awarded too.
The article contains the competition problems given at the 6th International Physics Olympiad (Bucharest, 1972) and their solutions. The problems were translated from the book published in Romania concerning the first nine International Physics Olympiads², because I couldn’t find the original English version.
¹ E-mail: popr@tvet.ro
² Marius Gall and Anatolie Hristev, Probleme date la Olimpiadele de Fizica, Editura Didactica si Pedagogica – Bucuresti, 1978
Условие
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 ε of the liquid, and the height H of the plates of the capacitor.
Discussion.
Отговори
Approximate result printed in the official solution for H much greater than h.
Решение
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:
Оригинал в Архива: ipho72.pdf