Abstract
The word technology may be in the talk of time for most individuals, however, little do they know what impacts all this development. The existence of visual systems, audio systems and other complex equipment all give credit to the early discoveries. Discovery of atoms, ions and later electrons simplified everything. It is from theses that energy was developed. One of the most promising techniques used by scientists is the charge to mass ratio of electrons. It helped in observing the nature of materials. This lab report aims at analyzing the Sir J. Thompson`s experiment of evaluating charge to mass ratio of an electron. It seeks to comprehend the influence of electric and magnetic fields on electron beams.
Introduction
While on his escapades, Sir J. Thompson realized that cathode rays were deflected while under a gradual application of electric and magnetic fields. He also realized for this to work, these fields had to be perpendicular to each other. His experiment led to the accurate determination of the charge to mass ratio of electrons. He proposed that; from the magnitudes of the applied fields one could easily calculate the e/m ratio of an electron.
Materials & equipment
- Assembled e/m tube and Helmholtz coils
- Ammeter
- Voltmeter
- Tape measure
- Supply voltage
- Connecting cables
Procedure
- Connect the e/m tube, and magnetic coils to the power supplies as advised. Turn on the accelerating voltage, let it warm for five minutes and apply 300V accelerating voltage.
- Turn on the power supply to the Helmholtz coils when the beam starts striking the helium atoms in the tube to 1.5Ampheres.
- Vary the coil diameters and note the changes.
- Vary the coil diameters from 11 cm to 5 cm in 1 cm increments, and then back to 11 cm, thereby taking two current readings at each selected diameter (go a little beyond 5 cm on the inward trip).
Set the coil current to 1.5 A.
- Collect data for various voltages and currents into the magnetic coils.
- Vary the diameter of the Helmholtz coils from 11cm to 5cm consequently and start it over again from 5. Tabulate your results
- Finally, carefully, rotate the entire apparatus through an angle of 180degrees, then repeat the above processes and table the results.
Experimental results
The table below shows results for the diameter of the rings
The table below shows results for the various variances and their derived data.
Results
F=Ma
Where B is the magnetic field (tesla), e is the magnitude of charge of an electron in (coulombs), and v is the velocity of the electron in (m/sec). The radius of the circle will be derived from the required centripetal force is presented by the magnetic force equation. Therefore
F=evB
evB=mv2r
v=(em)rB
Since this formula has e, m, and v as unknowns, one must eliminate v to realize the following ratio:
em =2vB2 r2
When a charged particle is moving in a uniform magnetic field, it is deflected to the region of low magnetism without any loss in energy, and causes the charge to move in arc that is segmented of a circle until the charge leaves the region. The electron is further accelerated out of the region by the magnetic field strength, which is obtained from the formulae below:
B=μₒnI a√4532
Where μₒ is the coefficient of permeability measured in webers (ampere meters) measured in teslas (weber/m2), n is the number of turns on the coils, while I is the current flowing in the coils (amperes).
The gradient dydx=br therefore when this ratio is arranged em =2vB2 r2 the following is realized
B2r2=2vme
Calculating the coefficient in equation 5
B=K*I where k=7.7*10^-4
B=7.7×100-4×1.5
μ=1.2152×10-4
Calculating e/m for part 1
We get
Sincev=150, and from graph, rB=5.5555×10-3
em=2×150(5.5555×10-3)2
em=9.729×10-6
Calculating e/m for part 2
em=2×31395.31.334025×10-6
=4.7068*10^10C/kg
Calculations of errors
1.7588*10^11-4.7068*10^10=1.28812*10^11
Percentage error for part 1
>100%
Percentage error for part 2
73.23% hence part 2 is more accurate in calculating the ratio of charge to mass.
The errors could have been as a result of faulty equipment or the fact that no real electrons or particles were used in this case.
Discussion and analysis
The data filled in this case for part one was used to find the value of B against 1/r. Computing the gradient of this line graph gives Br^2. The graph is a straight line but does not pass through the origin. From the gradient found in the experiment, it was possible to compute the ratio of charge to mass of an electron. The results would have been more accurate if the electric field had been used in place of the voltage. However, it is not possible due to the fact that the electric field requires the charge which had to be determined from the experiment.
For part 2, the graph was a straight line but not through the origin. The gradient of the curve gave v/r^2 which was used to compute the value of the ratio of charge to mass. The results were more accurate compared to part 1 though with a great percentage difference from the real value, which is because the errors could have arisen from the source potential difference or the eddy currents in the magnetic coils. There might be a systematic error have resulting from the assumption of the value of K, used to compute the magnetic field strength. The effect of the earth’s magnetic field can be explained using both Lenz’s law and Faradays law. Lenz’s law explains why the force felt on the apparatus was acting on the opposite direction. Faraday’s laws may be used to explain the relationship between magnetic field and electric field. The experiment is similar to one performed by J.J Thompson in which the velocity was found, and one by Millikan.
The values changed when the apparatus was rotated through 900 mainly because there were now two forces acting on the apparatus, the magnetic field and an electric field (Faraday’s laws of electromagnetism)
Conclusion
The main objective of the experiment was to find out the truth in Sir JJ Thompson experiment; objective achieved. It is evident that, rather than using electric field and magnetic field to estimate the e/m ratio, radii and potential difference on the same assembly could give the same results. The experiment also clearly showed the relationship between voltage, magnetic field and the radius used in the experiment.
In the real world, this experiment helps in determining the atomic structure of materials. For instance, in electricity, charge to mass ratio experiment will be useful in finding the properties of electrons and their ability to conduct electric current. It also assists in the manufacture of cathode ray equipment and vapor lamps.
Works cited
Serway, Raymond A., John W. Jewett, and Vahé Peroomian. Physics for scientists and engineers. 8th ed. Belmont, CA: Brooks/Cole, Engage Learning, 2010. Print.
Keller, Jaime. Theory of the electron: a theory of matter from START. Boston: Kluwer Academic Publishers, 2001. Print.
