Physics

Problem

Three electrons travel in vacuum along parallel lines that are all perpendicular to a fixed point P, as shown below in description form. • Electron A: distance from its path to P is

2.0\,\text{cm}

; speed

v_{A}=1.0\times10^{6}\,\text{m}\,\text{s}^{-1}

. • Electron B: distance from its path to P is

1.0\,\text{cm}

; speed

v_{B}=0.50\times10^{6}\,\text{m}\,\text{s}^{-1}

. • Electron C: distance from its path to P is

3.0\,\text{cm}

; speed

v_{C}=1.0\times10^{6}\,\text{m}\,\text{s}^{-1}

. For all three electrons, the velocity is perpendicular to the line that joins the electron to point P at the moment considered. (a) Rank the electrons from greatest to least according to the magnitude of the magnetic field each produces at point P. Clearly indicate any ties. (b) Electron A is accelerated so that its speed doubles while the other electrons are unchanged. Without doing detailed calculations, predict the new ranking of magnetic field magnitudes at P and justify your prediction. (c) Using the original speeds (before Electron A is accelerated), calculate the numerical ratio of the largest magnetic field magnitude at P to the smallest among the three electrons. Show your work.

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