In this lab a voltage drop V is used to accelerate electrons, and a current I fl

Question

In this lab a voltage drop V is used to accelerate electrons, and a current I flowing through Helmoltz coils is used to produce a magnetic field B that exerts the force causing electrons to travel on a circular orbit with radius r. Assume that V and I both have negligible uncertainties, i.e., delta V = 0 and delta l = 0. This means that a plot of V vs. (Ir)2 will need only "horizontal" error bars, i.e., the error bars for (lr)2 . To obtain the expression needed for the absolute uncertainty delta(lr)2 . requires use Eqs. (E.3) and (E.8) to get an expression for the relative uncertainty in (Ir)2 , and then use of Eq. (E.4) to convert it to the absolute uncertainty.

Explanation / Answer

since delta I = 0

so delta (I^2*r^2) / (I^2*r^2) = delta(r^2) /r^2 = 2r*delta(r) /r^2

= 2 delta(r)/r

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