e/m Ratio

Prelab

1.

2.

3.

Plot V vs D2, then the slope will contain e/m.

Uncertainties

There are two ways to calculate the uncertainty of B:

1. From definition of uncertainty (not suggested)

This is a hard way, and the next calculation method is suggested, see next paragraph.

For B = k I,

.

Since

,

then

,

then 𝛿B can be determined.

2. From the simplified equation for uncertainty (suggested)

Based on the "Error Propagation Analysis" document in the reference materials, use Eq. (0.3) and Eq. (0.4) for the multiplication and division of power-1 variables (i.e., not x2, z3, tn, where n ≠ 1, etc.),

.

Comparison of the Impact of R, n, and I.

Compare the coefficients of 𝛿n, 𝛿R, and 𝛿I, in the above equation, since the impact means that we should make the perturbation (i.e., uncertainty of R, n, and I) the same, and then compare the impacts.

For 𝛿n, 1/n = 1/131; 𝛿R, 1/R = 1/5; 𝛿I, 1/I = 1/1.5. So if the 𝛿's are the same, then 𝛿I dominates the uncertainty since 1/I is the largest.