FYKOS Year 29 Series 6 Problem 5 — Particle race · FYKOS 29 #29.6.5

Physics · mechanics · electromagnetism

Problem

Two particles, an electron with mass me=9,1⋅10−31  kgm_{e}=9,1\cdot 10^{-31}\;\mathrm{kg} and charge −e=−1,6⋅10−19C−e=-1,6\cdot 10^{-19}C and an alpha particle with mass mHe=6,6⋅10−27  kgm_{He}=6,6\cdot 10^{-27}\;\mathrm{kg} and charge 2ee, are following a circular trajectory in the xyxy plane in a homogeneous magnetic field B=(0,0,B0)\textbf{B}=(0,0,B_{0}), B0=5⋅10−5TB_{0}=5\cdot 10^{-5}T. The radius of the orbit of the electron is re=2  cmr_{e}=2\;\mathrm{cm} and the radius of the orbit of the alpha particle is rHe=200  mr_{He}=200\;\mathrm{m}. Suddenly, a small homogeneous electric field E=(0,0,E0)\textbf{E}=(0,0,E_{0}), E0=5⋅10−5V⋅  m−1E_{0}=5\cdot 10^{-5}V\cdot \;\mathrm{m}^{−1} is introduced. Determine the length of trajectories of these particles during in the time t=1  st=1\;\mathrm{s} after the electric field comes into action. Assume that the particles are far enough from each other and that they don't emit any radiation.

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