# 1 Measurement Of The Specific Charge Of An Electron (S.C.E.) By Alkis Vakalis.

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1 Measurement Of The Specific Charge Of An Electron (S.C.E.) By Alkis Vakalis

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

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. 3

There are three values which affect directly the S.C.E. : 1. The Radius R 2. The Magnetic Induction B 3. The Voltage V 4

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. B As we can see beside F the electron will move in a circuit due to the F centripetal force. e The radius R is defined by the F centripetal force and calculated by the type 1 U R B 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. B As we can see beside F the electron will move in a circuit due to the F centripetal force. e The radius R is defined by the F centripetal force and calculated by the type 1 U R B 5

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. 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. 6

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, the kinetic energy of the electrons will be equal to the potential energy. This relation is expressed through mathematics with the type 3 : 7

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 : 1. Voltage is equivalent to the S.C.E. 2. Magnetic induction,amperage and radius is conversely equivalent with S.C.E. 8

Εδώ θα μπει ένα print screen από το GeoGebra και μια μικρή επεξήγηση. 9

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For the laboratory experiment we need : 1. A round tube with mercury vapor at low pressure 2. 2 Helmholtz coils 3. 2 power suppliers 4. 1 DC power supplier for the coils 5. 1 digital Voltmeter to measure the advanced voltage 6. 1 digital Ammeter to measure the electric current 7. 1 mirror with predefined scales 8. Cables for the devices connections 11

V i B α β R Volt A cm m 130 1.5 180 1.5 230 1.5 280 1.5 330 1.5 220 1 1.2 220 1.5 220 1.7 220 2 12

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. 13

 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 http://en.wikipedia.org 14

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

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