Calculating e/m Ratio: A Puzzling Problem

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SUMMARY

The discussion centers on calculating the e/m ratio in an electron beam experiment, where the user has derived a gradient of 0.848 from a Voltage (V) versus Current (mA) graph. The formula used is e/m = (4.49*10^8 * gradient^2) / volts, with volts set at 3000. The calculated e/m value of 107625 C/kg is significantly lower than the expected value of 1.7*10^11 C/kg, indicating a potential issue with unit conversion or axis orientation in the graph.

PREREQUISITES
  • Understanding of electron beam experiments
  • Familiarity with graphing Voltage (V) against Current (mA)
  • Knowledge of unit conversion in physics
  • Proficiency in using the formula for calculating e/m ratio
NEXT STEPS
  • Review the principles of electron beam experiments
  • Learn about unit conversions between volts, amperes, and coulombs
  • Investigate common errors in plotting graphs for physics experiments
  • Study the derivation and application of the e/m ratio formula
USEFUL FOR

Physics students, experimental physicists, and educators involved in teaching or conducting electron beam experiments will benefit from this discussion.

barcelonaboy
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I'm trying to calculate the ratio of e/m, I've plotted the given data points to get a straight line graph with a gradient of 0.848.

I know that the ratio of e/m is given by e/m = (4.49*10^8 * gradient^2)/volts
where volts = 3000.

When I plug the numbers in I get a value of 107625 which is nowhere near the given book value of e/m 1.7*10^11 Ckg^-1

I think that I'm doing something in the wrong units as I need to get the answer in C/kg^-1, but I can't see where I'm going wrong.

Any pointers owuld be much appreciated
 
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I'm afraid that I don't know what you might be doing wrong because I don't know what data varibles you have. Are you plotting a current against a radius of a circle, or velocity against current flow, or voltage against current even I think can be one setup for an electron beam experiment.

Have you checked that your units are in the SI format?

Is your set of axis the right way round?

Yeah could do with some more info bud :(
Haths
 
Hi Haths,

I'm plotting a graph of Voltage (V) against Current (mA) (V/mA) as part of an electron beam experiment, which is giving a gradient of 0.848 with the R^2 coming out as 0.9991 which is a good fit for the data points, so I'm confident in the graph and the data points.

The equation that I need to plug my numbers into is, this includes the 4.49*10^8 as a dimensionless constant

e/m = (4.49*10^8)(gradient^2)(1/ 3000 volts)

I think that I'm going wrong on the units in the gradient as I can't see how to get from an equation that has units in volts and mA to one that involves Coulombs/kg or if there is some conversion factor that I'm not aware of.
 

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