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Unformatted text preview: Michael Lin Tuesday Section Partners: Josh Narciso, Bryant Rolfe Due Date: 3/7/07 E/M of the Electron Michael Lin The objective of this experiment was to measure the charge to mass ratio of the electron. Helmholtz coils were used to generate a uniform magnetic field that would create a force on electrons emitted from a heated filament, causing the electrons to move in a circular motion. By measuring the current and voltage in which the electrons are emitted and the diameter of the circular path it travels, the charge to mass ratio of the electron was estimated to be 1.63594E+11 C kg-1 , a 7.00% error from the actual charge to mass ratio of an electron. The earths magnetic field was approximated to be -3.07048E-05 T, a 12% error from the actual magnetic field. INTRODUCTION Electrons were first proven to all have the same charge to mass ratio by J.J. Thompson in 1897. Thompsons experiment, as in this experiment, uses the fundamental idea that a particle with charge e moving with a velocity v in a region with magnetic field B will feel a force given by the equation: F = ev x B ; where F, v, and B are vectors denoting their direction In a situation where the particle is traveling perpendicular to a perpendicular magnetic field, the force on the particle will cause it to move in a circle of radius r, where the plane of the circle is also perpendicular to B. The force due to the magnetic field can also be described as a centripetal force, as it moves the particle in a circular motion. Therefore, two equivalent equations to describe the force can be equalized: mv 2 /r = evB and this equation can be written to give the charge to mass ratio of the particle: e/m = v/(Br) Measurements of the velocity of the particle are often difficult, so it is more feasible to measure the potential difference V that accelerates the particle from rest to that unknown velocity. Using energy conservation, the velocity can be written in terms of the potential difference: (1/2)mv 2 = eV and this equation can be rewritten as: e/m = v 2 /2V By combining the two charge to mass ratio equations, the charge to mass ratio can be expressed only in terms of the potential difference in which the particle is accelerated. e/m = 2V/(B 2 r 2 ) In this experiment, a heated filament accelerates electrons perpendicular to a uniform magnetic field generated by Helmholtz coils, therefore causing the electrons to move in a circular path with the plane of the circle perpendicular to the magnetic field. The magnetic field generated by the Helmholtz coils in this particular experiment can be expressed by: B I = [4 * 10...
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