Find Maximum Velocity Range in Velocity Selector using Vmax and B values

[michael650]

I have a velocity selector that consists of two parallel plate capacitors each with a diameter of 20cm (L), and a distance between them d. The capacitors are connected to a power source that delivers a voltage V. A magnetic field goes into the selector and has a strength B. Given that d can be from 1mm to 10mm, B can be from 0 to 2Teslas, and there is a maximum voltage that the battery can put out (0V to V_max). With these parameters, I need to find the range of velocities that I can get out of a proton put into the velocity selector.



V_max = ( eB2Ld ) / ( m_p )

v_x = V/Bd


I have been working on this problem for a good few days now, and I've put in a tremendous amount of effort. It took me a long time to calculate the maximum voltage (which is 7.65x10⁵ V. With all the given parameters, and the second equation, I figured I would be able to find the range of velocities easily, but I was wrong. I noticed that I can get a velocity anywhere from 0 mps to an infinitely large one when insertting an incredibly small value for B (1x10^-30 Teslas). The numbers of this problem do not need to be realistic, they just have to work out mathematically

 

[Nate810]

. Therefore, I was wondering if there is any way to find the range of velocities without getting an infinitely large one? The range of velocities you can get out of a proton put into the velocity selector depends on the maximum voltage that the battery can put out and the strength of the magnetic field going into the selector. The maximum voltage (Vmax) is determined by the following equation: Vmax = (eB2Ld)/(mp), where e is the elementary charge, B is the magnetic field strength, L is the diameter of the parallel plate capacitors, d is the distance between them, and mp is the mass of the proton. Using this equation, you can calculate the range of velocities you can get out of the velocity selector by substituting in different values for the magnetic field strength B and maximum voltage Vmax. For example, if you set the magnetic field strength at 0 Teslas and the maximum voltage to 7.65x105 V, then the range of velocities you can get out of the velocity selector will be from 0 mps to 7.65x105 mps. If you increase the magnetic field strength to 1 Tesla and keep the maximum voltage the same, then the range of velocities you can get out of the velocity selector will be from 0 mps to 7.65x104 mps. In summary, the range of velocities you can get out of a proton put into the velocity selector depends on the maximum voltage that the battery can put out and the strength of the magnetic field going into the selector. By changing these two parameters, you can calculate the range of velocities you can get out of the velocity selector.