IYPT 1989, Задачи на турнира — Задача 15. Electron

Problems for the 2nd International Young Physicists’ Tournament

Critical edition

Olympiets Youth Center, Moscow, Soviet Union; March 24‒April 2, 1988 [1]

Critical edition: translated, restored, and commented text [2]

FINAL DRAFT. — Please do not re-publish. Suggestions and criticism welcome

Translated, edited and commented by Ilya Martchenko. The original edition’s historical notes, sources and acknowledgments are retained with problem 1.

Епиграф

Squamps are hunted from the inside only.
S. Lem [3]

Условие

An electron with a velocity of $v=3\cdot10^5\,\mathrm{m/s}$ flies with an impact parameter $d$ aside a metal ball with a radius of a few centimeters. [28] The charge of the ball changes with time under a law $q(t)=q_0\cos\omega t$, where $q_0=10^{-3}\,\mathrm C$, [29] $\omega=10^8\,\mathrm{s}^{-1}$. [30] Build a dependence plot of the deviation angle $\varphi$ of the electron on the impact parameter $d$. [31]

Note [28]

Not “a few centimeters”, but “1 cm”, at the Correspondence Round, according to Kvant magazine [Kvant 1988]

Note [29]

“$q_0=10^{-3}\,\mathrm C$”, according to 1990 Czech, Slovak and Hungarian texts. The value disputably reads either $q_0=10^{-3}\,\mathrm C$ either $q_0=10^{-8}\,\mathrm C$ in [Kvant 1988], q=10 Coulombs in the 1996 Czech text, and q=10 C in the 2006 English text. The value is entirely missing in [Jordens 1989]

Note [30]

“$\omega=10^{-8}\,\mathrm{s}^{-1}$”, according to the Hungarian text. “$\omega=10^8\,\mathrm{s}^{-1}$”, according to the Kvant, 1990 Czech, 1996 Czech, Slovak and the 2006 English text. The value is entirely missing in [Jordens 1989]

Note [31]

The Kvant version of the problem included the final question “Can this phenomenon be used to explain Compton scattering?” It is missing in [Jordens 1989], as well as in 1990 Czech, Slovak, Hungarian, 1996 Czech and 2006 English texts

Решение

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