Transcript Lecture24.ppt

Reflection &
Refraction,Reflected Images
Lecture 24
Monday: 12 April 2004
Chapter 35 Images
“Bar at the Folies-Bergere”
By Edouard Manet - 1882
Physical Principles of Design
Activity for Class 24 Monday: 12
April 2004
“e/m Ratio for the Electron”
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
 K   U  0 or  K    U
U  q V  (e) V 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
V = 100
initial
V = 50
V=0
e
1
2
m v 2  e V
Magnetic Force on a
Moving Charge (Review)

 
F  q vB
charge of the particle (C; + or –)
v : velocity of the particle (m/s)
B : magnetic field (T)
q:

 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
r
v
Although the directions of the vectors are
changing, the magnitudes stay the same.
v2
F  ma  m
r
F  qvB
v2
qvB  m
r
v2
mv
rm

qvB qB
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 v2  e V
2eV
v
m
or
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
mv
eB
e
v

m rB
2eV
m
2eV
e
2V
e
e 2V
m
m



m
rB
rB
m rB
v
2V
e

m
rB
2V
e

or
m r 2 B2
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