Measurement of Charge to Mass Ratio - Lab Report Example

Title Students Name Instructor’s name Institution Date Abstract Measurement of charge to mass ratio is not normally an easy task to find. Several experiments have to be conducted then, since the value for the charge is known, the mass ratio can be calculated or deduced from the graph. The current and voltage reading may be used with the kinetic energy .Using Newton’s second law, the ratio of charge to mass can be determined. There are two methods that may be used namely 1, the bush’s method and 1, the magnetron method. In the bush’s method, electron is moved to the anode from the cathode. There would be an electron released to the helium ray tube forming a visible circle. Taking into account the radius of the circle, the ratio of e/m can be determined. The knowledge about charge to mass ratio is of importance more so in the field of classical thermodynamics. This is so because, when an electric and magnetic field are subjected to two particles of the same charge to mass ratio, they move towards a common point. (Lorrain, & Lorrain, 2000) The experiment is possible because electron would have unique behavior when exposed to a magnetic field Introduction Busch method. The kinetic energy is normally equal to the product of charge and voltage. (1/2(mv2) =eV).A cathode ray oscilloscope is in use and serves the purpose of emitting electrons. The assumptions taken in the experiment are: The eV should be greater than the energy from which electron is emitted from the hot cathode and, the non relativistic expression for the particle should be considered. (Bleanly .B, & Bleanely, 1965) The voltage is maintained at a suitable range of about 200-1200 vs. α is the angle between the longitudinal axis of the tube and the trajectory of the electron. Having the angle α, the axial component is determined by taking vcosα whereas; transverse component is determined by vsinα. A force f is established when there is a uniform field B that is in the direction that is parallel to the longitude of the axis of tube. Therefore .This indicates that there is no work done meaning that, the kinetic energy would be constant. In addition the electron experiences a magnitude of  Experiment details The apparatus that come in handy include, helhotz coil cathode ray tube for emitting the electrons. The solenoid is positioned centrally to the cathode ray tube and tilted at 63°C. The voltage of about 600 volts is used. The brightness is adjusted to give the minimum beam intensity .then the current coil is raised till the first spot is noted on its initial loci and coil currents readings noted. Repeat the same procedure to the next deflection points. This is done so for a varying voltage of about 100v to 1200v.The varying solenoid current is made for the accelerating voltage. When the beam spot is minimized, the values are noted. Magnetic field is determined from the current obtained that will aid in the calculations of e/m The apparatus set up is as shown Fig 1 Results 1. Busch’s Method VH= 600V n I1(Amps) I2(Amps) Average (Amps) I2(A) 1 1.37 1.34 1.355 1.83 2 2.84 3.04 2.94 8.64 3 4.05 4.11 4.08 16.65 VH= 700V n I1(A) I2(A) Average (A) I2(A) 1 1.49 1.47 1.48 2.19 2 3.08 3.15 3.115 9.70 3 4.40 4.32 4.36 19.00 VH= 800V n I1(A) I2(A) Average (A) I2(A) 1 1.60 1.57 1.585 3.42 2 3.27 3.36 3.315 10.99 3 4.70 4.45 4.575 20.93 VH= 900V n I1(A) I2(A) Average (A) I2(A) 1 1.68 1.68 1.68 2.82 2 3.47 3.48 3.475 12.08 3 4.71 4.71 4.71 22.18 VH= 1000V n I1(A) I2(A) Average (A) I2(A) 1 1.79 1.85 1.82 3.31 2 3.61 3.62 2.615 6.84 3 4.70 4.71 4.705 22.14 VH= 1100V n I1(A) I2(A) Average (A) I2(A) 1 1.88 1.87 1.875 3.52 2 3.84 3.78 3.81 14.52 3 4.70 4.68 4.69 22.00 The tabulates data gives the graph as follows From the equation  (Bleanly .B, & Bleanely, 1965) This leads to b to be 7.88 The slope of the graph gives the value of e/m to be 1.639344c/k Discussion when current is applied to helium coil it creates a magnetic field which eventually causes deflection of electron beam. The value of the e/m should be about one half with the error of about 6%.However constant current gives a percentage error of about 1.2%.This indicates the charge to mass ratio of the graph may be closely to the calculated value. Some systematic and random errors at times occur due to environmental effects, physical setup of apparatus and the earth’s magnetic field. The actual expected value should be about 1.7c/kg. (Lorrain, & Lorrain, 2000) However the percentage error of about 1.98 %deters the experimental value from attaining the actual value. Magnetron effect This is another method that is used the performance of this experiment. It uses a grd7 which is a diode with concentric electrodes. The cathode radius is less than that of the anode. When acted upon by a magnetic field by placing a solenoid that coincides with the electrode axis. There is a force which is perpendicular to the field of the coil (b) and the velocity (v) the electrons then flows in a curved path from the cathode to the anode. The increase in flux increases proportionally with the curve. When the field is greater than the critical value; the anode current stops flowing. Experiment details A grd7 anode a power supply is used. Also a solenoid is used which is associated with a power supply. The diode is mounted to be in the centre of the solenoid, the filament current is set at 2.2A and it’s kept constant. The anode voltage is adjusted to 60v, and then the coil current is raised periodically while the anode current values are noted. This is done till the current has dropped to zero. The electric field radius is given by.   Positive potential of the anode with respect to the cathode. Electron would have acceleration if they are near the cathode because r (a)>>r (o).This leads to 1/2mv2==eva (Maxwell, 1954) Results 1. The data from the experiment Magnetron Effect is tabulated to make the analysis that would aid in getting the e/m ratio Tables of coil current I and the anode current IA: VA= 60V I (mA) IA (Amps) 500 0.021 525 0.020 550 0.018 575 0.015 600 0.012 625 0.009 650 0.006 675 0.004 700 0.002 725 0.001 750 0.001 755 0 VA= 80V I (mA) IA (Amps) 600 0.022 625 0.021 650 0.020 675 0.018 700 0.016 725 0.012 750 0.009 755 0.006 800 0.004 825 0.002 850 0.001 875 0.0005 900 0 VA= 100V I (mA) IA (Amps) 700 0.022 725 0.021 750 0.020 775 0.019 800 0.017 825 0.014 850 0.010 875 0.007 Now perform the experiment by holding the coil current steady and changing the anode voltage until the anode current has diminished. Coil current = 700 VA (Volts) I A (Amps) Ic((A) Ic2(amps)2 100 0.018 0.006 0.000036 95 0.0145 0.0048 0.000023 90 0.011 0.0036 0.000013 85 0.007 0.0023 0.0000052 80 0.004 0.0013 0.0000069 75 0.002 0.0006 0.00000036 70 0.001 0.0003 0.00000009 65 0 0 0 Discussion The space charge affects the electron energy distribution for the anode voltage measurement is conducted at 60 v, 80v and 100v.measurement of anode currents are taken in respect to coil current. A curve obtained using mat lab exhibits the value found are slightly below the expected values by a small fraction. (Bleanly .B, & Bleanely, 1965) It’s also known that the energies are almost half the value of the anode and are not the same as the accelerating voltage. This is so as the overall mean energies is far much below the maximum anode due to the electron collision within space charge. The errors may occur in these experiments as a factor of many causes. For instance, the earth’s magnetic field is very close to the field of the equipment. This closeness could cause interference with the experiment. This should be avoided by inclining the apparatus at some angle. In addition, the initial thermal velocity spectrum of electron being emitted may not come out perpendicularly. This calls for various data to be collected to get a correlation of the data. The anode at times may not be a perfect cylinder causing the magnetic field not to be distributed equally. The cathode may at times not lie along the centre of the anode making fewer electrons reaching the anode. The cut off current of about 0.67A is observed. The long solenoid equation helps in the determination of charge to mass ratio more so when we have the number of turns and the coil distance. Conclusion Generally these experiments aid in the determination of charge to mass ratio. Several experiments have been conducted such as Millikan and have also given approximately the same values. The value of charge to mass ratio is important in classical physics as it helps in study of electrons. Answers Why reversing the current increases accuracy Reversing the current makes the error that may occur due to the apparatus to be overcomed.Both direction current has the effect of cancellation of any magteic effect. The electrons that do not reach the anode get ionised leaving only the rest to be deflected. The constant curent method is superior because contant voltage method doesn’t give way for the intreception of the electron at the inner pins.It therefore becomes a challenge to get the ratio of e/m. References Maxwell, J. (1954). A treatise on electricity and magnetism. Canada: General publishing Bleanly .B, I, & Bleanely, B. (1965). Electricity and magnetism. Oxford: Clarendoson. Lorrain, P, & Lorrain, F. (2000). Fundamentals of electromagnetic phenomena. 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his indicates the charge to mass ratio of the graph may be closely to the calculated value. Some systematic and random errors at times occur due to environmental effects, physical setup of apparatus and the earth’s magnetic field. The actual expected value should be about 1.7c/kg. (Lorrain, & Lorrain, 2000) However the percentage error of about 1.98 %deters the experimental value from attaining the actual value. Magnetron effect This is another method that is used the performance of this experiment.

It uses a grd7 which is a diode with concentric electrodes. The cathode radius is less than that of the anode. When acted upon by a magnetic field by placing a solenoid that coincides with the electrode axis. There is a force which is perpendicular to the field of the coil (b) and the velocity (v) the electrons then flows in a curved path from the cathode to the anode. The increase in flux increases proportionally with the curve. When the field is greater than the critical value; the anode current stops flowing.

Experiment details A grd7 anode a power supply is used. Also a solenoid is used which is associated with a power supply. The diode is mounted to be in the centre of the solenoid, the filament current is set at 2.2A and it’s kept constant. The anode voltage is adjusted to 60v, and then the coil current is raised periodically while the anode current values are noted. This is done till the current has dropped to zero. The electric field radius is given by.   Positive potential of the anode with respect to the cathode.

Electron would have acceleration if they are near the cathode because r (a)>>r (o).This leads to 1/2mv2==eva (Maxwell, 1954) Results 1. The data from the experiment Magnetron Effect is tabulated to make the analysis that would aid in getting the e/m ratio Tables of coil current I and the anode current IA: VA= 60V I (mA) IA (Amps) 500 0.021 525 0.020 550 0.018 575 0.015 600 0.012 625 0.009 650 0.006 675 0.004 700 0.002 725 0.001 750 0.001 755 0 VA= 80V I (mA) IA (Amps) 600 0.022 625 0.021 650 0.020 675 0.018 700 0.016 725 0.012 750 0.009 755 0.006 800 0.004 825 0.002 850 0.001 875 0.0005 900 0 VA= 100V I (mA) IA (Amps) 700 0.022 725 0.021 750 0.020 775 0.019 800 0.017 825 0.014 850 0.010 875 0.007 Now perform the experiment by holding the coil current steady and changing the anode voltage until the anode current has diminished.

Coil current = 700 VA (Volts) I A (Amps) Ic((A) Ic2(amps)2 100 0.018 0.006 0.000036 95 0.0145 0.0048 0.000023 90 0.011 0.0036 0.000013 85 0.007 0.0023 0.0000052 80 0.004 0.0013 0.0000069 75 0.002 0.0006 0.00000036 70 0.001 0.0003 0.00000009 65 0 0 0 Discussion The space charge affects the electron energy distribution for the anode voltage measurement is conducted at 60 v, 80v and 100v.measurement of anode currents are taken in respect to coil current. A curve obtained using mat lab exhibits the value found are slightly below the expected values by a small fraction.

(Bleanly .B, & Bleanely, 1965) It’s also known that the energies are almost half the value of the anode and are not the same as the accelerating voltage. This is so as the overall mean energies is far much below the maximum anode due to the electron collision within space charge. The errors may occur in these experiments as a factor of many causes. For instance, the earth’s magnetic field is very close to the field of the equipment. This closeness could cause interference with the experiment.

This should be avoided by inclining the apparatus at some angle. In addition, the initial thermal velocity spectrum of electron being emitted may not come out perpendicularly. This calls for various data to be collected to get a correlation of the data. The anode at times may not be a perfect cylinder causing the magnetic field not to be distributed equally. The cathode may at times not lie along the centre of the anode making fewer electrons reaching the anode. The cut off current of about 0.

67A is observed.

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