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Up: 4.2 Procedure Previous: 4.2.4 Calculations

4.2.5 Errors

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 tex2html_wrap_inline239 , tex2html_wrap_inline241 , tex2html_wrap_inline243 and tex2html_wrap_inline245 , where Z = e/m, then the error in e/m is given by:

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if the errors are random, not systematic. Evidently, if a small change is made in one of the independent variables, e.g., a change tex2html_wrap_inline253 in the value of V, then the resulting change in tex2html_wrap_inline257 will be given by:

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Compute tex2html_wrap_inline239 , using a typical set of data to evaluate tex2html_wrap_inline263 and estimating tex2html_wrap_inline253 from the least count (smallest division) of the voltmeter. Evaluate tex2html_wrap_inline241 resulting from the uncertainty tex2html_wrap_inline269 in I, using the test of reproducibility made in the measurements. Obtain tex2html_wrap_inline243 resulting from the spread in values of tex2html_wrap_inline197 observed above. Finally, estimate tex2html_wrap_inline277 , the uncertainty in r, and find tex2html_wrap_inline245 . 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.