Figure 27.42 shows schematically part of the apparatus used in 1897 by J. J. Thomson to determine the charge-tomass ratio of the electron. A beam of electrons, all moving at the same speed \(v\), enters a region of electric and/or magnetic fields. When an electric field of magnitude \(1.0 \mathrm{kV} / \mathrm{m}\) and a magnetic field of magnitude \(1.2 \times 10^{-4} \mathrm{~T}\) are turned on, the electrons go through the device undeflected. When the magnetic field is turned off, the electrons are deflected by \(3.2 \mathrm{~mm}\) in the negative \(y\) direction after traveling the length \(\ell=0.050 \mathrm{~m}\) of the apparatus. Given that the charge of the electron is \(-e=-1.60 \times 10^{-19} \mathrm{C}\), what is the mass of each electron?

Data from Figure 27.42

Transcribed Image Text:

v x B out of page 11 path with B or Ay on path with B off