Deflection of an electron beam by electric field Follow the method to calculate how the voltage between the vertical plates varies the height of the election beam in the region between the plates. Method: 1- your Crooked tube is similar to the CRT of an oscilloscope. The main difference being that your tube has no horizontal deflectors, only vertical ones. The electron gun (“C”) is used to accelerate electrons. Draw a diagram of the barrel and deflector plates. Represent an electron coming out of the barrel with a horizontal velocity v0. 2- Assuming no deviation, trace the trajectory of the election between the plates. The undeflected position of the electron beam will serve as a reference. Suppose now that the electron, while crossing the plates, is deflected upwards. The vertical difference between the two points of impact on the TRC screen is the delta y deviation that we are looking for. If the electron is deflected upward, what is the orientation of the electric field between the plates? 3- Using the laws of kinematics, write an equation giving the time t necessary for the electron to cross the plates (of length d). We will suppose that the electric force, consequence of the field between the plates, is the only one which acts on this electron. 4- Still with the laws of kinematics, now write an equation giving the deviation delta y (from step 2) as a function of the acceleration undergone by the electron during its passage between the plates, as well as the crossing time . We will assume here that the deflector plates are uniformly loaded infinite flat plate. 5- Now combine the two previous equations to obtain the deviation as a function of the acceleration. In this equation, replace the acceleration with an equation involving the electric field. 6- The relation between the voltage delta V and the electric field E and the distance which separates the plates h is: delta Vdev = E*h. Use this relationship to replace E in your equation. 7- Use the following relation to replace v0 in your equation: q deltaVacc = (1/2)*m*(v0)^2. In other words, you must make sure that the initial velocity v0 does not appear in your final equation. 8- What kind of relationship do you get between the delta y deflection and the delta deflection voltage Vdev (linear, quadratic, etc.)? 9- What type of relation do you get between the delta y deviation and the delta deviation voltage Vacc (linear, quadratic, etc.)?
Deflection of an electron beam by electric field
Follow the method to calculate how the voltage between the vertical plates varies the height of the election beam in the region between the plates.
Method:
1- your Crooked tube is similar to the CRT of an oscilloscope. The main difference being that your tube has no horizontal deflectors, only vertical ones. The electron gun (“C”) is used to accelerate electrons. Draw a diagram of the barrel and deflector plates. Represent an electron coming out of the barrel with a horizontal velocity v0.
2- Assuming no deviation, trace the trajectory of the election between the plates. The undeflected position of the electron beam will serve as a reference. Suppose now that the electron, while crossing the plates, is deflected upwards. The vertical difference between the two points of impact on the TRC screen is the delta y deviation that we are looking for. If the electron is deflected upward, what is the orientation of the electric field between the plates?
3- Using the laws of kinematics, write an equation giving the time t necessary for the electron to cross the plates (of length d). We will suppose that the electric force, consequence of the field between the plates, is the only one which acts on this electron.
4- Still with the laws of kinematics, now write an equation giving the deviation delta y (from step 2) as a function of the acceleration undergone by the electron during its passage between the plates, as well as the crossing time . We will assume here that the deflector plates are uniformly loaded infinite flat plate.
5- Now combine the two previous equations to obtain the deviation as a function of the acceleration. In this equation, replace the acceleration with an equation involving the electric field.
6- The relation between the voltage delta V and the electric field E and the distance which separates the plates h is: delta Vdev = E*h. Use this relationship to replace E in your equation.
7- Use the following relation to replace v0 in your equation: q deltaVacc = (1/2)*m*(v0)^2. In other words, you must make sure that the initial velocity v0 does not appear in your final equation.
8- What kind of relationship do you get between the delta y deflection and the delta deflection voltage Vdev (linear, quadratic, etc.)?
9- What type of relation do you get between the delta y deviation and the delta deviation voltage Vacc (linear, quadratic, etc.)?
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