Балкански 2008, Теория — Задача 2. Exercise 1

Concours Général de Physiques « Minko Balkanski » — 17 May 2008 · 17 май 2008 г.

Указания

The main problem and the three exercises are completely independent and can be solved in any order.

All the answers must be given in English or French. The clarity and precision will be taken into account for the final note.

The exam is 4 hours long! The calculators are authorized.

Условие

Let’s consider a beam of electrons, which is propagating in a vacuum with a speed $\vec{V}$, electronic density $\rho$ and radius R.

1.) Considering only the electromagnetic interactions, calculate the expression of the magnetic and electrostatic fields created by the electrons as a function of $\varepsilon_0$, $\mu_0$, $\rho$, R, $\vec{V}$ and r (the distance to the center of the beam). We can ignore the side effects and suppose that the beam has the form of an infinite cylinder.

2.) Making a balance of all forces try to find out the sense of evolution of the radius of the electronic beam in the time.

Hint: The speed of light in the vacuum is $c = \dfrac{1}{\sqrt{\varepsilon_0\times\mu_0}}$, with $\varepsilon_0 = 8{,}85.10^{-12}\ SI$, $\mu_0 = 4\pi\times10^{-7}\ SI$

Решение

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Оригинал в Архива: CGP_2008_en.pdf