Lecture 24
Monday: 12 April 2004

“Bar at the Folies-Bergere”
By Edouard Manet - 1882

Physical Principles of Design
Activity for Class 24 Monday: 12
April 2004
J.J.Thomson-Experiment

Joseph John (“J.J.”) Thomson
J.J. Thomson
1856-1940
J.J. Thomson was appointed in 1884 as the third Cavendish Professor (head of the Cavendish Laboratory) at Cambridge, after James Clerk Maxwell and Lord
Rayleigh. In 1899, his experiments with cathode ray tubes led him to postulate the existence of a new particle with a ratio of charge to mass (e/m) far larger than the same ratio for a positive hydrogen ion.
The word “electron” was coined in 1891 by G. Johnstone Stoney.
Today we will measure e/m for the electron.

Calculating Change in K.E.
from Electric Potential (Review) final e

V = 100
V = 50 e
 initial

K
 
U

0 or
U
 q V

(
 e ) V

K
  
U or

U

(
 e )

V

K
 
(
 e )(

V )

( 1 .
6

10

19
) ( 100 )


1 .
6

10

17
J
If the electron starts at rest (or very close to it), then
1
2 m v
2  e

V
V = 0

Magnetic Force on a
Moving Charge (Review)

F
 q
 v


B
 charge of the particle (C; + or –) v
B
: velocity of the particle (m/s)
: magnetic field (T)

Force is at a right angle to velocity.

Force is at a right angle to magnetic field.
Important: If q is negative, that reverses the direction of force.

The Radius of the Circle (Review)
F v r
Although the directions of the vectors are changing, the magnitudes stay the same.
F
 m a
F
 q v B
 m v 2 r q v B
 m v
2 r r
 m q v
2 v B
 m v q B

Apparatus for Measuring e/m
We will set

Potential in tube (V).

Current in coils (I).
We will observe

Radius of circular electron path (r).
We will calculate
 e/m.

The Cathode Ray Tube
Electrons
Electrons are randomly kicked out of the metallic cathode by thermal energy.
Once free of the metal, the electrons are accelerated through a potential difference of

V from cathode to anode.

Analysis of Electron Acceleration cathode anode
Electron Stream pot = -V pot = 0

K
  
U

U

(
 e )

V

K
 
(
 e )[

V ]
 e [ 0

(

V )]
 e V
Electrons have very low kinetic energy when they leave the cathode – essentially zero.
1
2 m v
2  e V or
2 e V v
 m

Helmholtz Coils
Magnetic
Field
Helmholtz Coils are designed to have a nearly uniform (constant) magnetic field in the center. The field direction is along the axis of the coils. The magnitude is proportional to I, the current. The formula to calculate this is a Physics 2 topic, but for our coils,
B

7 .
8

10

4
I where B is in tesla and I is in amperes.

Derivation of e/m Formula r
 m v e B e m
 v r B v
 e m

2 e V m
2 e V m r B
 e m

2 V r B or e m r B
2 V
 e m
 r
2
2 V
B
2 e m
2 V r B
We set or observe all of the variables on the right side of the equation.

Experimental Procedure
1.
Turn up V to get an electron beam. Record V.
2.
Turn up I (to make B) until the electrons make a complete circle.
Record I.
3.
Observe r – use the mirrored scale in the rear.
3a.
Or (easier): Adjust I until the electrons just hit the far side of the tube. This is a known radius
(5.5 cm). Record I.
4.
Repeat three times with different values of V.

Viewing the Electron Path