GeoGebra 20-20 STEM Challenge

1. GeoGebra 20-20 STEM Challenge Measurement Of The Specific Charge Of An Electron (S.C.E.) By Alkis Vakalis

2. Synopsis In this project we will measure the specific charge of an electron (S.C.E.) in different rates of a homogenous magnetic field. Moreover, throughGeoGebrawe will replicate the movement of an electron inside the magnetic field and visualize the changes which are caused to it’s orbit.

3. Measuring the S.C.E. of an electron: We are going to determine the charge-to-mass (e/m) ratio by Lenard’s method of measuring a beam of electrons (the cathode ray) bent into a circular path by a known homogenous magnetic field. The value of e/m can be determined from the radius of curvature of the path of the electrons.

4. The Direct Factors There are three values which affect directly the S.C.E. : • The Radius R • The Magnetic Induction B • The Voltage V

5. Theory Assume that an electron e moves with speed U vertically to a magnetic induction B so that they create an 90° angle. When the electron E enders the magnetic field accepts a force F (Lorenz force) which determines it’s orbit. BAs we can see beside F the electron will move in a circuit due to the F centripetal force. eThe radius R is defined by the F centripetal forceand calculated by the type 1 UR B

6. Theory The Magnetic Induction is defined by the Amperage i in the coils and is measured indirectly by the type 2 : ****** while the rate of the Voltage V is solely determined by us.

7. The Electrical Field How it affects the electrons? • The electrical field is responsible for the acceleration of the electrons. If the electrical potential difference of the cathode and the anode is V then ,according to the conservation of energy, thekinetic energy of the electrons will be equal to the potential energy. This relation is expressed through mathematics with the type 3 :

8. The Equation In order to be able to measure the S.C.E. we must generate an equation which will be consist of our already known values. Through the combination of the types 1 & 3 we get the below type with which we can measure the S.C.E. indirectly with the type 4 : From the above type we can understand that : • Voltage is equivalent to the S.C.E. • Magnetic induction ,amperage and radius is conversely equivalent with S.C.E.

9. In GeoGebra Εδώ θα μπει ένα printscreen από το GeoGebra και μια μικρή επεξήγηση.

10. The experiment

11. The experiment For the laboratory experiment we need : • A round tube with mercury vapor at low pressure • 2 Helmholtz coils • 2 power suppliers • 1 DC power supplier for the coils • 1 digital Voltmeter to measure the advanced voltage • 1 digital Ammeter to measure the electric current • 1 mirror with predefined scales • Cables for the devices connections

12. The measures we need

13. What we do The previous chart shows the measures we have to take, notice that : • In the first 5 measures we keep Amperage stable in order to determine the effects of Voltage to the S.C.E. • Accordingly in the last 5 measures we keep voltage stable in order to determine the effects of Amperage to the Magnetic Induction and consequently to the S.C.E. • In order to measure the points of α and β we will use the mirror from our components. • Then we measure the Radius R through our known type • Eventually, we measure the S.C.E. with the type 4 and complete the chart.

14. Bibliography & Sources • Albert P. Malvino (2006), Electronic Principles • Randall D. Knight (2008), Physics for Scientists and Engineers Volume A’ • Randall D. Knight (2008), Physics for Scientists and Engineers Volume B’ • Dimitrios Kehrakos and Nikolaos Mouftis (2008), Manuals Of Physic Laboratory • http://en.wikipedia.org

15. Many thanks to.. My mentoring team : Nikolaos Matzakos Dimitrios Kehrakos Kalliopi Kounenou Nikolaos Mouftis and the GeoGebra Institute of Athens , Greece