# Physics307L F09:People/Gleicher/e/m

## e/m Lab Summary

For this lab, the objective is to try to measure the value of the ratio of an electron's charge to its mass. The experiment is detailed here in the manual [1] under e/m.

Using the setup detailed in the manual, we varied one the parameters while keeping the other one constant and then measuring the radius of the electron beam.

The calculation of e/m involves the value of the accelerating voltage, current, and the radius of the electron beam. The formula for e/m is given by:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{q}{m}=\frac{2*V}{r^2*B^2}}**
.

The value for the B field can be calculated by the formula given in the manual:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle B=7.8E-4 * I}**

If the voltage (V), current (I), and radius (r), are known we can determine the vale of e/m.

### Procedure

Mike and I kept the voltage constant and varied the current while monitoring r, then we kept current constant and varied the voltage while recording the radius.

The first value of e/m involves direct calculation from the values of the accelerating voltage, the current, and the radius of the electron beam.

A plot of r vs. 1/I at constant V will give a value of e/m when a linear least squares fit is performed.

The last value of e/m can be obtained form another linear least squares fit of a plot of r^2 vs. V at constant I.

### Data

The data can also be found in my notebook Physics307L_F09:People/Gleicher/Notebook/071022

Constant Current:

I (A) | V | R (cm) |
---|---|---|

1.52 | 296 | 6 |

1.52 | 311 | 6.3 |

1.52 | 325 | 6.15 |

1.52 | 340 | 6.65 |

1.52 | 355 | 6.6 |

1.52 | 370 | 6.5 |

1.52 | 385 | 6.8 |

1.52 | 400 | 6.9 |

1.52 | 416 | 7 |

1.52 | 430 | 7 |

1.52 | 445 | 7 |

1.52 | 454 | 7 |

Constant Voltage:

I (A) | V | R (cm) |
---|---|---|

2.25 | 454 | 6.5 |

2.1 | 454 | 5.25 |

1.95 | 454 | 5.9 |

1.79 | 454 | 6.25 |

1.65 | 454 | 6.37 |

1.50 | 454 | 6.75 |

1.35 | 454 | 7.25 |

1.2 | 454 |

### Results

Thanks to Linh Le's write up, I was able to resolve my error for the calculation of e/m.

The first calculated value is 1.09E+11 Coulombs/kg. I am not sure how to calculate the error in this measurement.

^{SJK 00:31, 5 December 2007 (CST)}

^{SJK 00:33, 5 December 2007 (CST)}(1.51202 +/- .179)E+11 Coulombs/kg

My third value for e/m is

(1.88E +/- .646)E+11 Coulombs/kg

^{SJK 01:02, 5 December 2007 (CST)}

### Conclusions

Initially my data was flawed but after obtaining the right formula for q/m from Lihn Le's page, and analyzing my graphs properly, I was able to end up with three reasonable values for q/m.

My value for the third calculation is the best. This one involved plotting r vs. I^-1.

^{SJK 00:46, 5 December 2007 (CST)}Possible explanations for the discrepancy include stray magnetic fields, systematic error in the procedure (data aquisition), and incorrect values given for the calculation of the B field.

Here is a link to my excel file with the calculations: