Transcript Document

Hw: All Chapter 2 problems and exercises
Reading: Chapter 3
Example 4: Electric field on ring’s
axis
z

E
1
Qz
40 ( z 2  R 2 ) 3 2

iz
Example 6: Electric field on disk’s
axis
   z
z

E


2
2
2 0  z 2
z R
z

z  R, z  0 E 

xdx
( x  c)
2
3
2
1

( x  c)
2
1
2

iz


Q
i
2 z
40 z
1
  z 
z  R E 
iz
2 0 z
  
z0 E
iz
2 0

 
z0 E
iz
2 0
Exercise 5 page 33
In a famous experiment Millikan
measured the size of the electron’s

charge by adjusting an E field so that the force of gravity pulling
down on a small, charged oil drop was cancelled by the electric force
pushing up. If the mass of the drop was 2.0 10 13
kg and it
contained 10 electronic charges, what size E field was necessary
to keep the drop in equilibrium?
Robert Millikan’s oil-drop experiment (1909)
Robert Andrews Millikan
1868-1953
American experimental physicist
1923 Nobel Prize
Millikan received a Bachelor’s degree in the classics from Oberlin
College in 1891 and his doctorate in physics from Columbia
University in 1895 – he was the first to earn a Ph.D. from that
department.
"At the close of my sophomore year [...] my Greek professor [...]
asked me to teach the course in elementary physics in the
preparatory department during the next year. To my reply that I
did not know any physics at all, his answer was, 'Anyone who
can do well in my Greek can teach physics.' 'All right,' said I, 'you
will have to take the consequences, but I will try and see what I
can do with it.' I at once purchased an Avery’s Elements of
Physics, and spent the greater part of my summer vacation of
1889 at home – trying to master the subject. [...] I doubt if I have
ever taught better in my life than in my first course in physics in
1889. I was so intensely interested in keeping my knowledge
ahead of that of the class that they may have caught some of my
own interest and enthusiasm."
Exercise 5 page 33
In a famous experiment Millikan
measured the size of the electron’s

charge by adjusting an E field so that the force of gravity pulling
down on a small, charged oil drop was cancelled by the electric force
pushing up. If the mass of the drop was 2.0 10 13
kg and it
contained 10 electronic charges, what size E field was necessary
to keep the drop in equilibrium?
Motion in an electric field
A positively charged object, with
 mass m, is placed
at rest in a constant
field. EHow fast will the
object be moving after it has traveled a distance
L?
Example 2
Consider a constant, vertical electric field
somehow created in a limited region of space. An
electron enters the region traveling horizontally
with speed v0 . If the region has a length L, how
much will the electron be deflected at the end of
the region?
Example 3
A particle with mass m and charge q is ejected
from the lower of two parallel plates with velocity
of magnitude v0 as shown. If a constant electric
field exists between the plates, magnitude E,
where will the particle return to the lower plate?
How large must L be so that the particle doesn’t
strike the upper plate? (Neglect gravity.)
y
E
v0

L
x
P218 Review: Conservative forces
One-dimensional problem:
x2
x2
dU
dx   [U ( x2 )  U ( x1 )]
W   F ( x)dx   
dx
x1
x1
dU
F ( x)  
dx
Two-dimensional problem:

r2

r2

r2

r1

r1

r1
 
W   F dr   Fx dx   Fy dy
Fx  
W
W
conservative
conservative


 [U (r2 )  U (r1 )]
U
U
; Fy  
x
y
does NOT depend on path!
around the closed path is zero!
Have a great day!
Please don’t
pictures
forget
your
Hw: All Chapter 2 problems
and exercises
Reading: Chapter 3