I've been working on this problem for awhile but I just can't seem to hack it. (This is problem 76 from Serway 3rd for the first electricity chapter if you happen to have that book and want a visualization)(adsbygoogle = window.adsbygoogle || []).push({});

Given: an electron with charge, -e, and mass, m, is projected with speed v, at a right angle to a uniform electric field that is flowing in the negative y direction. The oscilloscope has length d, and after the particle exits the field it travels a length, L, and smacks a screen. It was displaced in the positive y direction to a height of h when it has hit the screen. Assuming d is much less than L in magnitude, and ignoring gravity, show the charge-to-mass ratio is given by:

e/m = hv^2/(ELd)

First, I set Ee = ma and divide through to get e/m = a/E

Solving for a in terms of L, d, and h, I know the electron is travelling with constant horizontal velocity, and it travels a distance of (L + d) in time t, or

v = (L+d)/t so t = (L+d)/v

I also know that it is accelerating in the y direction, so

h = vyt + 1/2at^2 (there is no initial y component to the velocity so...)

h = .5at^2

plugging in for t and solving for a I get...

2h/(L+d)^2/v^2 = a which simplifies to 2hv^2/(L^2+2dL+d^2) = a

I then plug it into the original ratio equation

e/m = 2hv^2/(E(L^2+2dL+d^2) which assuming d is much less than L,

e/m = 2hv^2/(E(L^2 +2dL) which is close but not the answer

If anyone can help me I would be greatly appreciative. I know I have probably made a stupid mistake somewhere, but for the life of me, I can't find it. Thank you.

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# Homework Help: Charge to mass ratio of an electron shot through a cathode-ray oscilloscope

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