Is the m/e Equation Valid When F = 0 in J. J. Thomson's Experiment?

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In J. J. Thomson's experiment, if the net force (Fnet) is zero, the velocity (v) can be expressed as E/B, allowing for the measurement of the mass-to-charge ratio (m/e). However, the assumption that F = 0 raises concerns about the change in y, suggesting it should also be zero, which would make the denominator of the m/e equation zero and invalidate it. This leads to a contradiction in the equation's validity. The discussion centers on whether this reasoning is flawed or if the equation can still hold under these conditions. Clarifying this point is essential for understanding the implications of Thomson's findings.
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Homework Statement
The statement is below.
Relevant Equations
F = qv × B
20191021_145637.jpg
20191021_145723.jpg
The text showed if Fnet = 0 (with F from magnetic fields and electric field), then v = E/B . And we can measure m/e (last equation in the image).

My question is, by assuming F = 0, change in y should also be 0 , so the denominator of right side of the m/e equation must be zero. And the equation doesn't hold. Am I wrong?
 
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Samanko said:
My question is, by assuming F = 0, change in y should also be 0 , so the denominator of right side of the m/e equation must be zero. And the equation doesn't hold. Am I wrong?

That's ##y## from the first case with ##E## only.
 

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