This demonstrates the practical method of determining charge to mass ratio. This experiment is generally undertaken in the first year of an engineering degree program.

1. CONCEPT BY :-
SACHIN MOTWANI
PRASHANT MALIK
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 1

2. Around 1890s, mass of electron?
Magnitude of Charge on electron =1.6 × 10−19
C
Corollary:
𝑚 𝑒 =
𝑒
𝑒 𝑚 𝑒
Significance of e/m?
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 2

3. Sir Joseph John Thomson
(1856-1940)
English Nobel Laureate in Physics
Discovery: Electron, Sub-atomic Particles ,
Isotopes
Best known for: Plum Pudding Model of Atom
One of the notable students: Neils Bohr
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 3

4. Prerequisite Knowledge
Lorentz Force?
Motion of a charged particle, moving through a
combination of electric and magnetic fields;
F = qE + q v x B
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 4

5. Apparatus
Cathode Ray Tube
Power Supply Unit
Pair of Bar Magnets
Magnetometer
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 5

6. ScCathode Ray Tube
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 6

7. Applications of CRT
CRT Screens Televisions &
Computers
CRT X-Ray Machine
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 7

8. Magnetometer
 Extremely Sensitive
 Perhaps, needs enclosure in
an insulated Chamber during
Experiments.
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 8

9. Theory
High voltage applied across electrodes.
Gas b/w electrodes ionized.
-ve particles (electrons or cathode rays)
formed after ionization, attracted towards
anode.
Phosphorescent coated screen gets bright
spot on beam strike.
Scale measures deflection of the beam.
At no Electric or Magnetic field, beam
travels straight line without deflection.
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 9

10. During Electric Field alone:-
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 10

11. During Magnetic Field alone:-
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 11

12. Both Electric and Magnetic Fields simultaneously:-
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 12

13. When sufficient potential (V) is applied between the two electrodes, electrons emitted from the cathode
accelerate with velocity ‘v’ then,
Hence, the specific charge at the electron is determined if the values of E, B, and V are known.
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 13

14. Formula Used
𝑒
𝑚
=
𝑉𝑌
𝜇0
2 𝐻𝑒
2
tan2 𝜃 𝐿 +
𝑙
2
𝑙𝑑
𝐶/𝑘𝑔
Symbol Meaning Standard Values for available
apparatus (units)
V Voltage Applied across plates (Volts)
Y Total deflection of spot on screen (metre)
𝜇0 Permittivity of free space 4𝜋 × 10−7
H/m
𝐻𝑒 Horizontal Component of Earth’s
Magnetic Field in that Latitude &
Longitude
26 nanoTesla
(New Delhi)
𝜃 Deflection of needle 𝑑𝑒𝑔𝑟𝑒𝑒
l Length of horizontal pair of plates in CRT 25mm
L Distance of the screen from the edges of
plates
130mm
d Separation between the deflecting plates 10𝑚𝑚
# Be sure to convert all Values to the SI units!
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 14

15. Effect of Earth’s Magnetic Field
East-West or West-East
direction.
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 15

16. DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 16

17. DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 17

18. The Standard value of e/m of electron by J.J. Thomson
method is 1.756 × 1011 C/kg.
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 18

19. Corollary of the Result
Particles with mass lower than the atoms, discovered.
The mass of electron could ow be calculated as :-
𝑚 𝑒 =
𝑒
𝑒 𝑚 𝑒
=
1.6022 × 10−19
𝐶
1.756 × 1011
= 9.1 × 10−31
𝐾𝑔
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 19

20. HOTS Question
Both the electric and magnetic fields can deflect a charged particle. What is difference in these
deflections?
A. The force acting on the charged particle in a magnetic field is velocity dependent. The
direction of force acting on the moving charge is perpendicular to both the direction of motion
of the charged particle and the direction of magnetic field, and the magnetic force depends on
the angle between the direction of motion of particle and the direction of magnetic field. The
force on the stationary charged particle is zero. The work done on the particle by the magnetic
field is zero, hence the kinetic energy of the particle is unaffected. On the other hand, the force
acting on the charged particle in an electric field is velocity independent. The direction of force
is always in the direction of electric field whatever may be the direction of motion of particle.
The kinetic energy of particle, therefore changes.
DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 20

21. DETERMINATION OF CHARGE TO MASS RATIO BY J.J. THOMSON'S METHOD. 21