Electrons

Thermionic EmissionDeflection of Electrons in Electric FieldDeflection of Electrons in Magnetic FieldDetermination of e/mCathode Ray Oscilloscope

Thermionic Emission (1)

When a metal is heated sufficiently, its free electrons gain enough kinetic energy to leave the metal. This process is called thermionic emission.

Thermionic Emission (2)

In practice, thermionic emission is caused by heating a filament of metal wire with an electric current.

Thermionic Emission (3)

The work done on each electron from the filament isW = eV where V is the p.d. across the filament and the anode.

Electron-voltThe electron-volt is an amount of energy equal to the work done on an electron moved through a p.d. of 1V.

19106.1 1 electron-volt = J

Properties of Electron Beams (Cathode rays)

Cathode rays travel in straight lines. Cathode rays can cause fluorescence. Cathode rays can be deflected by electric

field and magnetic field. Cathode rays may produce heat and X-rays. Cathode rays can affect photographic plates.

Deflection of Electrons in a Uniform Electric Field (1)

Consider an electron beam directed between two oppositely charged parallel plates as shown below.

With a constant potential difference between the two deflecting plates, the trace is curved towards the positive plate.

+

-

d

Deflection of Electrons in a Uniform Electric Field (2)

The force acting on each electron in the field is given by

d

eVeEF P

where E = electric field strength, V = p.d. between plates, d = plate spacing.

p

Deflection of Electrons in a Uniform Electric Field (3)

The vertical displacement y is given by

22 )(2

1

2

1t

md

eVaty p

2

2

)(2

1

v

x

md

eVp

This is the equation for a parabola.

Deflection of Electrons in a Uniform Magnetic Field (1)

The force F acting on an electron in a uniform magnetic field is given by

BevF

Since the magnetic force F is at right angles to the velocity direction, the electron moves rounda circular path.

Deflection of Electrons in a Uniform Magnetic Field (2)

The centripetal acceleration of the electrons is

m

Beva

Hence m

Bev

r

va

2

which gives

eB

mvr

Determination of Specific Charge - e/m

J. J. Thomson

Determination of Specific Charge Using a Fine Beam Tube (1)

The principle of the experiment is illustrated by the diagram below.

× × × × × × × ×× × × × × × × ×× × × × × × × ×× × × × × × × ×× × × × × × × ×

vF=Bev

Electron gun

r

Determination of Specific Charge Using a Fine Beam Tube (2)

and the kinetic energy of the electron providedby the electron gun is

eVmv 2

2

1

Where V is the anode voltage.

m

Berv (For an electron moving in a

uniform magnetic field)Since

Determination of Specific Charge Using a Fine Beam Tube (3)

Rearrange the equation gives

22

2

rB

V

m

e

The value of the specific charge of an electronis now known accurately to be

1110)000003.0758803.1( C/kg

eVm

Berm 2)(

2

1So

Thomson’s e/m Experiment (1)

Thomson’s apparatus for measuring the ratio e/m

× × × × × × × × ×× × × × × × × × ×× × × × × × × × ×× × × × × × × × ×

+

-

v

Thomson’s e/m Experiment (2)

A beam of electron is produced by an electron gun with an accelerating voltage V.

The electron beam is arranged to travel through an electric field and a magnetic field which are perpendicular to each other.

The apparatus is set-up so that an electron from the gun is undeflected.

Thomson’s e/m experiment (3)

As the electron from the gun is undeflected, this gives

BE FF

i.e. BeveE B

Ev

On the other hand, eVmv 2

2

1

Combining the equations, we get2

2

2VB

E

m

e

Bev

eE

v

Cathode Ray Oscilloscope (CRO)

The structure of the cathode ray tube

Uses of CRO

An oscilloscope can be used as

1. an a.c. and d.c. voltmeter,

2. for time and frequency measurement,

3. as a display device.

Lissajous’ Figures (1)

Lissajous’ figure can be displayed by applying two a.c. signals simultaneously to the X-plates and Y-plates of an oscilloscope.

As the frequency, amplitude and phase difference are altered, different patterns are seen on the screen of the CRO.

Lissajous’ Figures (2)

Same amplitude but different frequencies

Lissajous’ Figures (3)

Same frequency but different phase

In phase π/2 π 3π/2 In phase

π /4 3π/4 5π/4 7π/2

http://surendranath.tripod.com/Lissajous/Lissajous.html