There are four quantities needed in order to compute e/m.
Errors in each of these
contribute to the error in e/m.
If the four resultant errors in e/m are denoted by
,
,
and
,
where Z = e/m, then the error in e/m is given by:
if the errors are random, not systematic.
Evidently, if a small change is made in one of
the independent variables,
e.g., a change in the value of V,
then the resulting change
in
will be given by:
Compute , using a typical set of data to evaluate
and estimating
from
the least count (smallest division) of the voltmeter.
Evaluate
resulting from the
uncertainty
in I,
using the test of reproducibility made in the measurements.
Obtain
resulting from the spread in values of
observed above. Finally, estimate
,
the uncertainty in r, and find
.
As a help in estimating: suppose this distance were
known to six significant figures;
would the experiment by improved?
The answer is of course no. Why?
Which is the largest source of error in e/m? Discuss the possible systematic errors.
Discuss the observed fluctuation in your values of e/m in light of the above remarks.