In this lab you will get an experimental value for the ratio e/m for the electro

Question

In this lab you will get an experimental value for the ratio e/m for the electron from the slope s of a graph. You will use the relationship e/m = slope/const In the above equation the constant term const has an uncertainty A(const) due to uncertainty Aa in the measurement of the radius a of the Helmholtz coils that produce the magnetic field B. Since the value of const depends on radius a as a2, and all the other terms in const are free of may be used to show that the relative error for the term const uncertainty, equation calculate the relative error of e/m in terms of Use equations (Note: You must use the substitutions Deltas for Deltas , the absolute uncertainty in the slope s , and Delta a for Delta alpha, the absolute uncertainty in the radius a .

Explanation / Answer

so

d(e/m)/(e/m) = sqrt( (dconst/const)^2 + (ds/s)^2)

but dconstant/const = 2 da/a

so d(e/m)/(e/m) = sqrt( ( 2 da/a)^2 + (ds/s)^2)

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