Having trouble linearizing an equation

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SUMMARY

The forum discussion focuses on the linearization of the equation for measuring the ratio of charge to mass for electrons (e/m) and the ambient magnetic field of the Earth (BE). The user presents the equation e/m=2v/[(BH-BE)^2]*r^2 and seeks a more effective method for linearization. The derived form, BH=[(2vm/e)^1/2]*1/r + BE, is confirmed as the only viable solution for expressing BH. The discussion emphasizes the importance of clarity in mathematical notation to avoid ambiguity.

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Homework Statement


The goal of my lab was to measure the ratio of charge to mass for electrons (e/m) and the approximate ambient magnetic field of the Earth (BE). I have come up with what is the required equation (my TA confirmed this) but I am having trouble linearizing it.

y=mx+b
y=(e/m)x+BE

While the answer I have would work, I can't help but feel that there is a better way to linearize this equation. Any help would be appreciated.

Homework Equations



e/m=2v/[(BH-BE)^2]*r^2

The Attempt at a Solution



e*(BH-BE)^2/m=2v/r^2

(BH-BE)^2=2vm/er^2

BH-BE= (2vm/er^2)^1/2

BH=[(2vm/er^2)^1/2] +BE

BH=[(2vm/e)^1/2]*1/r +BE
 
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If you want to solve that equation for BH, there is no possible other result (apart from more complicated ways to write the same thing).

Be careful with written fractions - 1/ab is ambiguous. A computer would interpret it as (1/a)*b, and some human readers get confused. If you mean 1/(ab), the brackets are important.
 

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