How should I calculate the error in my e/m ratio calculation for my homework?

In summary, the problem at hand involves finding the e/m ratio of the electron using a given formula. The difficulty lies in calculating the error for the calculation, as two different methods were used to measure and record results. The current method being used for calculating error results in a high percentage error, but it is suggested to use only the errors from the gradient of the graphs, leading to a lower overall error. The correct method for calculating error in this situation is unclear.
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Phystudent91
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Homework Statement


I'm in the middle of a project finding the e/m ratio of the electron by the use of the formula below. I know all required values and can find a result, I'm unsure how to calculate an error for the calculation.
In the formula below, D, n, A and f are all given quantities (therefore no error/the error can be taken as 0, right?)

Homework Equations



[itex]\frac{e}{m}[/itex] = (32/D2)*(nA2∏)2*(Va/Is2)*(Is/Vs)2

The Attempt at a Solution



The last 2 parts of the equation are where the trouble arises. I have had to measure and record results in two different ways to find values and to plot the 2 graphs - Va/Is2 and Is/Vs - and the software used gives a percentage error in the line.
Do I need to find the error in each measurement for Va and Is etc?

The current way I know to calculate error would mean using the smallest value measured and half of the smallest possible measurement (half the equipment increment). This would result in a stupidly high error, eg:
smallest V measurement was 5V, this is also the smallest increment on the equipment, therefore error is ±2.5V meaning an error in that set of measurements of 50%??
I'm then taught to add the percentage errors... this leads to 350% error.
However, because I know the gradients of the graph, is it acceptable to only use these errors? This would give a total are of ≈10%. Much better!

Which is the correct way of going about this? And if the answer is neither of these, what is the correct way of going about this!?

Thanks in advance!
 
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  • #2
Any Help would be appreciated!
 

Related to How should I calculate the error in my e/m ratio calculation for my homework?

1. What is the first step in finding an error in calculation?

The first step is to double check your work and make sure that you have entered all the numbers and equations correctly. It is important to pay attention to details and avoid simple mistakes.

2. How do I know if there is an error in my calculation?

You can compare your answer with a known solution, use a calculator or computer program to verify your work, or ask a colleague to review your calculation. If your answer does not match the expected result, there may be an error in your calculation.

3. What should I do if I find an error in my calculation?

If you find an error, the first step is to identify where the mistake was made. This could be a simple transcription error or a more complex mathematical error. Once you have identified the error, correct it and recheck your work to ensure that the final answer is accurate.

4. How can I prevent errors in my calculations?

To prevent errors, it is important to be organized and systematic in your approach to calculations. Double check all numbers and equations, use a calculator or computer program when possible, and ask for help or a second opinion if you are unsure about a calculation.

5. What are some common types of errors in calculations?

Some common types of errors include transcription errors, calculation errors, and rounding errors. Transcription errors occur when numbers or equations are written or entered incorrectly. Calculation errors can happen when the wrong formula is used or when there is a mistake in the calculation process. Rounding errors occur when numbers are rounded to the wrong decimal place or when rounding is done incorrectly.

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