geogebra 20-20 stem challenge

15
GEOGEBRA 20-20 STEM CHALLENGE 1 Measurement Of The Specific Charge Of An Electron (S.C.E.) By Alkis Vakalis

Upload: giulio

Post on 06-Jan-2016

44 views

Category:

Documents


1 download

DESCRIPTION

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

TRANSCRIPT

Page 1: 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

Page 2: GeoGebra 20-20 STEM Challenge

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, 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.

Page 3: GeoGebra 20-20 STEM Challenge

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.

Page 4: GeoGebra 20-20 STEM Challenge

4

The Direct Factors

There are three values which affect directly the S.C.E. :

1. The Radius R2. The Magnetic Induction B3. The Voltage V

Page 5: GeoGebra 20-20 STEM Challenge

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.

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

Page 6: GeoGebra 20-20 STEM Challenge

6

Theory

The Magnetic Induction is defined by the Amperage i in the coilsand is measured indirectly by the type 2 :

  ******

while the rate of the Voltage V is solely determined by us.

Page 7: GeoGebra 20-20 STEM Challenge

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

Page 8: GeoGebra 20-20 STEM Challenge

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

equivalent with S.C.E.

Page 9: GeoGebra 20-20 STEM Challenge

9

In GeoGebra

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

Page 10: GeoGebra 20-20 STEM Challenge

10

The experiment

Page 11: GeoGebra 20-20 STEM Challenge

11

The experiment

For the laboratory experiment we need :

1. A round tube with mercury vapor at low pressure2. 2 Helmholtz coils3. 2 power suppliers 4. 1 DC power supplier for the coils5. 1 digital Voltmeter to measure the advanced voltage6. 1 digital Ammeter to measure the electric current7. 1 mirror with predefined scales8. Cables for the devices connections

Page 12: GeoGebra 20-20 STEM Challenge

12

The measures we need

V i B α β R

Volt A cm cm m

130 1.5

180 1.5

230 1.5

280 1.5

330 1.5

220 1

220 1.2

220 1.5

220 1.7

220 2

Page 13: GeoGebra 20-20 STEM Challenge

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.

Page 14: GeoGebra 20-20 STEM Challenge

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

Page 15: GeoGebra 20-20 STEM Challenge

15

Many thanks to..

My mentoring team :

Nikolaos Matzakos Dimitrios Kehrakos Kalliopi Kounenou Nikolaos Mouftis

and the GeoGebra Institute of Athens , Greece