PCS 130 Lab report 1 Charge to Mass Ratio

in kilograms or grams, “v” is the velocity of the particle measured in meters per second, and “r” represents the radius which is measured in centimeters or meters. The velocity of the charged particle depends on its kinetic energy. The kinetic energy of the charged particle and the conservation of energy can be reduced to its electric potential energy which has been expressed by this equation below: By examining the relationship between the kinematics energy and its particle, an equation can be found to calculate the charge to mass ratio of the particle. Materials ● Meter Stick ● Wooden Cover to block out light ● Banana Cables ● Set of Helmholtz Coils ● Low Voltage Variable Power Supply for Helmholtz Coils ● High Voltage Power Supply for accelerating Voltage ● Tube Procedure Before touching any equipment, be sure that the power supply is shut off to keep out of danger. The radius of the coils was given in the lab manual to prevent any damage to the apparatus in a potential attempt of recording this value yourself. Turn on the power supply, begin with a low current to check if the apparatus is in function. Increase the voltage until a beam is visible in the apparatus, this is the electron accelerating. Once everything is set and ready, proceed to change the current, doing this alters the radius of the electron beam. Change the current 10 times while recording the diameter of each trial.

Given: B = 2.84 × 10 − 3 T e = 1.60 × 10 − 19 C m = 9.12 × 10 − 31 Kg ΔV = 250 volts r 2 = 2 ( e m ) ΔV ( 1 B 2 ) r 2 = 2 ( 1.60 × 10 − 19 9.12 × 10 − 31 ) 250 ( 1 ( 2.84 × 10 − 3 ) 2 ❑ ) r 2 = 1.08 × 10 19 ❑ Figure 3: Sample calculation of r^2 value from trial 1 Charge to mass ratio (e/m) of an electron: The slope of the graph in “figure 1” should represent the mass to charge ratio of an electron, therefore, to get the charge to mass ratio of an electron we can simply take the reciprocal of the slope value. slope = m e = 1.18 × 10 − 10 e m = 1 1.18 × 10 − 10 = 8.47 × 10 9 C Kg Percent error: % error = | Theoreticalvalue − Experimentalvalue | Theoreticalvalue × 100 % error = | 1.76 × 10 11 − 8.47 × 10 9 | 1.76 × 10 11 × 100 % error = ¿ 95% Therefore, this experiment was extremely inaccurate. Some errors that may have occurred during the lab could be incorrect values of diameter. Another error that could have occurred can be the equipment, there may have been potential dysfunctions in the apparatus that was used to conduct the experiment. The voltage may have been too low while doing the experiment, this could have resulted in errors as well.

References 1. Randall Dewey Knight. (2017). Physics for scientists and engineers a strategic approach 4th edition Pearson 2. Lab 1 - Charge to mass ratio of the electron