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0 Plate Plate m,Q x=L x (a) Assume that the weight of the electron can be neglected, so that the only force in play is the electric force. Derive an expression (in terms of the given variables E, L, y, and vo) for this ratio of the electron charge to its mass, m/Q showing and explaining all your steps. Hint: this is very similar to a kinematics/free fall problem, two dimensional motion under the influence of a constant force, with the constant acceleration a determined by the electric force instead gravity. Additional hints are provided in the homework guide at the end of this document. (b) Look up the charge and mass of the electron and design an experiment (choose values for E, L, and vo that give a reasonable deflection y.) We do want to make sure the electric force is much larger than the gravitational force on the electron. Note that electron velocities can be very close to the speed of light, since the electron mass is so very small.

0 Plate Plate m,Q x=L x (a) Assume that the weight of the electron can be neglected, so that the only force in play is the electric force. Derive an expression (in terms of the given variables E, L, y, and vo) for this ratio of the electron charge to its mass, m/Q showing and explaining all your steps. Hint: this is very similar to a kinematics/free fall problem, two dimensional motion under the influence of a constant force, with the constant acceleration a determined by the electric force instead gravity. Additional hints are provided in the homework guide at the end of this document. (b) Look up the charge and mass of the electron and design an experiment (choose values for E, L, and vo that give a reasonable deflection y.) We do want to make sure the electric force is much larger than the gravitational force on the electron. Note that electron velocities can be very close to the speed of light, since the electron mass is so very small.

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The charge to mass ratio of the electron was first measured by J. J. Thompson in 1897. This is often referred to as THE discovery of the electron. Thompson used a combination of electric and magnetic fields in his experiment. We will defer the magnetic part of the experiment to later in the course, and examine the electric part now. The device he used sent a beam of electrons between two plates, as shown below, between two plates. The initial velocity, vo of the beam was horizontally to the right. Thompson then measured the deflection, y, of the beam from where it exited the plates with the electric field turned off. Thompson also used a magentic field, which allowed him to determine the initial velocity. For now, lets find an expression for the charge to mass ratio in terms of this velocity and the other parameters. y JE Plate Plate m, Q x=L x (a) Assume that the weight of the electron can be neglected, so that the only force in play is the electric force. Derive an expression (in terms of the given variables E, L, y, and vo) for this ratio of the electron charge to its mass, m/Q showing and explaining all your steps. Hint: this is very similar to a kinematics/free fall problem, two dimensional motion under the influence of a constant force, with the constant acceleration a determined by the electric force instead of gravity. Additional hints are provided in the homework guide at the end of this document. (b) Look up the charge and mass of the electron and design an experiment (choose values for E, L, and vo that give a reasonable deflection y.) We do want to make sure the electric force is much larger than the gravitational force on the electron. Note that electron velocities can be very close to the speed of light, since the electron mass is so very small.
Transcribed Image Text:The charge to mass ratio of the electron was first measured by J. J. Thompson in 1897. This is often referred to as THE discovery of the electron. Thompson used a combination of electric and magnetic fields in his experiment. We will defer the magnetic part of the experiment to later in the course, and examine the electric part now. The device he used sent a beam of electrons between two plates, as shown below, between two plates. The initial velocity, vo of the beam was horizontally to the right. Thompson then measured the deflection, y, of the beam from where it exited the plates with the electric field turned off. Thompson also used a magentic field, which allowed him to determine the initial velocity. For now, lets find an expression for the charge to mass ratio in terms of this velocity and the other parameters. y JE Plate Plate m, Q x=L x (a) Assume that the weight of the electron can be neglected, so that the only force in play is the electric force. Derive an expression (in terms of the given variables E, L, y, and vo) for this ratio of the electron charge to its mass, m/Q showing and explaining all your steps. Hint: this is very similar to a kinematics/free fall problem, two dimensional motion under the influence of a constant force, with the constant acceleration a determined by the electric force instead of gravity. Additional hints are provided in the homework guide at the end of this document. (b) Look up the charge and mass of the electron and design an experiment (choose values for E, L, and vo that give a reasonable deflection y.) We do want to make sure the electric force is much larger than the gravitational force on the electron. Note that electron velocities can be very close to the speed of light, since the electron mass is so very small.
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