Charge to Mass

Introduction

In the lecture we have explored the intricacies in the relationship between electricity and magnetism. We learned that magnetic fields can impart forces onto electrically charged objects, and that the movement of charged particles can induce magnetic fields. The objective of this experiment is to experimentally determine the charge:mass ratio of a beam of electrons, and compare this to tabulated values. We can use a Helmholtz coil and a mercury vapor chamber to visualize a beam of electrons, and obtain data from them.

Experimental Method

Align a Helmholtz coil containing a mercury vapor chamber so the device points Northward with an angle of inclination of 18 degrees upward from the horizontal. Set the voltage of the EMF for the coil to between 20-40V (we used 30V), and adjust the current in the loops using an ammeter. Inside the mercury vapor chamber should be an ‘electron gun’ with a variable voltage, independent of the Helmholtz device. This voltage can be adjusted to supply the electrons with more or less kinetic energy - by varying the speed of the electrons within the magnetic field, we can use circular motion equations to describe their trajectory. Relating the force of the magnetic field on the electron to centripetal force, and measuring the radius of curvature of the beam allows us to experimentally derive the charge:mass ratio of the electron. All calculations were derived from the following set of EM equations:

B=8/125Rμ0NI q/m = v/rB Ep = Ek Ek= 0.5mv2 PE=12QV

We used these equations to calculated the charge:mass ratio for 5 independent trials at the same voltage (same velocity of electrons) and calculated the average charge:mass ratio.

Results

Radius of curvature (m) | Voltage (V) | Current (A) | B Field (T) | Q:m (C/Kg) |

0.065 | 30 | 3.26 | 1.84x10-4 | 1.92x1011C/kg |

0.078 | 30 | 2.77 | 1.56x10-4 | 1.89x1011C/kg |

0.090 | 30 | 2.40 | 1.35x10-4 | 1.89x1011C/kg |

0.103 | 30 | 2.11 | 1.19x10-4 |...