A proton enters the gap between a pair of metal plates (an electrostatic separator) that produces a uniform, vertical electric field between them. Ignore the effect of gravity on the proton.
a) Assuming that the length of the plates is 11.1cm , and that the proton will approach the plates at a speed of 18.3km/s , what electric field strength should the plates be designed to provide, if the proton must be deflected vertically by 1.19⋅10−3rad?
b) What speed does the proton have after exiting the electric field?
c) Suppose the proton is one in a beam of protons that has been contaminated with positively charged kaons, particles whose mass is 494 MeV/c2 (8.81⋅10−28kg) , compared to the mass of the proton, which is 938 MeV/c2 (1.67⋅10−27kg) . The kaons have +1e charge, just like the protons. If the electrostatic separator is designed to give the protons a deflection of 2.65⋅10−3rad, what deflection will kaons with the same momentum as the protons experience?
The Attempt at a Solution
The process was to equate the force of the proton to the electric field strength times the charge on the proton.
First we find the time it takes for the proton to travel between the length of the plates.
v=x/t → t=x/v = 6.0656*10-6s
the deflection s
s=[itex]\phi[/itex]x = 0.00119*(18300)2 = 398519.1m
to find our acceleration we take s/t2
From our (mpap)/qp=E
(1.67*10-27kg)(3.5905*106m/s2)/(1.6067*10-19C) = E
I used the motion equation to get the vertical acceleration
since initial y velocity is zero...
To get the total magnitude of the velocity in the x and y direction...
This is where I don't know how to proceed. If I am still dealing with the same basic setup since the problem states that our setup has been contaminated to include kaons and not a different situation, the only values that change are mass and velocities.
Since the problem asks what the deflection would be if the kaon had the same momentum as the proton, I tried
and I solved for the velocity required of the kaon to have the same momentum as the proton.
My question is if it is the same process as in part a except that I just change the values for mass, velocity, set [itex]\phi[/itex] = 0.00265 rad and solve for s?
Thank you any help is appreciated.