From last time…
Electric fields
A
B
Electric field
lines
Feb. 13, 2008
Physics 208 Lecture 7
1
Exam 1 , Wed. Feb. 20, 5:30-7 pm
Alternate exam time for students Wed. Feb. 20, 2:30-4
with class conflicts: Wed. Feb. 20, 6-7:30
To attend alternate exam, you must email me with 1) your conflict, 2) which exam
Covers Chap. 21.5-7, 22-23,25-26
+ lecture, lab, discussion, HW
8 1/2 x 11 handwritten note sheet (both sides) allowed
Review Group/Quiz (solutions on website).
Review lab question sheets.
Review sample exams on website.
Week5 HW (avail. this Thurs, due Fri. next week)
covers exam material.
Feb. 13, 2008
Physics 208 Lecture 7
2
Friday Guest Lecture
Prof. Thad Walker
UW Physics
“Holography”
Feb. 13, 2008
Physics 208 Lecture 7
3
Superposition of electric fields

Electric field from a point charge:
Q
Q
ˆ
Ek 2r
rˆ
2
r
4o r


1 
k 

 4 o 
From a set of point charges:
Superpose E-fields from
 individual charges


Feb. 13, 2008
Physics 208 Lecture 7
4
Charge Densities

Volume charge density: when a charge is distributed
evenly throughout a volume
  = Q / V
dq =  dV

Surface charge density: when a charge is distributed
evenly over a surface area
  = Q / A
dq =  dA
Linear charge density: when a charge is distributed along
a line
  = Q /
dq =  d

Feb. 13, 2008
Physics 208 Lecture 7
5
Infinite line of charge
An infinite line of charge has a uniform charge density
 Coulombs / meter. What direction is the electric
field at point x?
B.
C.
x
A.
D.
E.
+ + + + + + + + + + + + + + + + + + +
Feb. 13, 2008
Physics 208 Lecture 7
6
E-field: infinite line of charge
dE y  cosdE
y


dE
2
r 2  x
dQ  dx

r
1
4 o

dQ
r2  x 2
dQ

4 o r 2  x 2

2
1

1
cos
r
r2  x 2
rdx
4 o r 2  x 2 3 / 2
+ + + + + + + + + + + + + + + + + + + +
x


Charge density Coulombs/meter
Feb. 13, 2008
Physics 208 Lecture 7
7
Add all these up
Ey 

 2 4
0
rdx
1
o
r
2
x

2 3/2


xdx




 2k
1/ 2
2
2
2o rr  x 
r
2o r
0

Units?
Feb. 13, 2008


Physics 208 Lecture 7
8
Finite line of charge
What direction is the
E-field above the
end of the line
charge?
C
B
A
D
E
+ + + + + + + + + + + + + + + + + + + +
Feb. 13, 2008
Physics 208 Lecture 7
9
Ring of uniform positive charge
Which is the graph of the
y
field on the axis?
A)
x
B)
C)
D)
E)
Feb. 13, 2008
z
Physics 208 Lecture 7
10
Quick quiz
We have an infinite sheet of charge of uniform
charge density . The electric field
A. increases with distance from plane
B. decreases with distance from plane
C. is independent of distance from plane
D. changes direction with distance from plane
Feb. 13, 2008
Physics 208 Lecture 7
11
E-field of plane of charge

Text does this as adding up rings of charge.

E plane 
2o
  Surface charge density


Feb. 13, 2008
Physics 208 Lecture 7
12
Electric fields and forces


Original definite of E-field was
(Coulomb Force) / charge
E-field produced force on charged particle.
F  qE
Feb. 13, 2008

Physics 208 Lecture 7
13
Quick Quiz
A negative charge in outer
space is in a uniform E-field
that points to the right.
What is the motion of the
particle?
Fe
-
Uniform E
A) Moves right at constant speed
B) Moves left at constant speed
C) Remains stationary
D) Accelerates to the left
E) None of the above
Feb. 13, 2008
Physics 208 Lecture 7
14
Force on charged particle





Electric field produces force
qE on charged particle
Force produces an acceleration a = FE / m
Uniform E-field (direction&magnitude)
produces constant acceleration
Positive charge accelerates in direction of the field
Negative charge accelerates in direction opposite
the electric field
Feb. 13, 2008
Physics 208 Lecture 7
15
Electron in a Uniform Field


The electron is projected
horizontally into a uniform
electric field
The electron undergoes a
downward acceleration


It is negative, so the
acceleration is opposite E
Motion is parabolic while
between the plates
Feb. 13, 2008
Physics 208 Lecture 7
16
Quick Quiz
A negative charge is released in a fluid with a uniform Efield that points to the right. The fluid imparts a force
proportional to and opposite to the velocity F fluid  -bv
What is the motion of the particle?
A. Accel left continuously
B. Accel left,
then moves at const. speed
 F
e
C. Accel left, then slows to stop
D. Accel left, then turns around
-
Fluid
Uniform E
E. None of the above
Feb. 13, 2008
Physics 208 Lecture 7
17
Motion of charged particle

If no other forces, positive charge accelerates
in direction of E-field.

But many systems have drag forces
(e.g. molecules in a liquid, etc)

Drag force is complex, but
usually depends on velocity.

Particle reaches
terminal velocity,
determined by force balance
Feb. 13, 2008
Physics 208 Lecture 7
18
Application: Gel Electrophoresis







Charged macromolecules in ‘gel’ with applied E-field
Electric force: FE = qE Steady state: F +F =0
E
D
Drag force: FD ~ -cv
v = qE / c
Speed depends on
charge and drag (molecule size)
Sometimes too complex to interpret
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Protein electrophoresis:
soak in detergent to give proteins
all the same charge density.
Result, small proteins move faster
Feb. 13, 2008
Physics 208 Lecture 7
19
Isoelectric focusing





Separate macromolecules by
charge, not size
Macromolecules put
in solution of linearly varying pH
Electric field applied
Charge on molecule depends on local pH
Molecules move until no more force at their isoelectric point
Feb. 13, 2008
Physics 208 Lecture 7
20
Quick Quiz
An electric dipole is in a uniform electric field as
shown. The dipole
Dipole
A. accelerates left
B. accelerates right
C. stays fixed
D. accelerates up
E. none of the above
Feb. 13, 2008
Physics 208 Lecture 7
21
Electric torque on dipoles
  r  F ,
F  qE, r  s/2
F-  -qE, r  s/2


magnitude rF sin 
Total torque has magnitude

  qsE
r-
r

Dipole moment has magnitude
p  qs


Torque on dipole
in uniform field

Feb. 13, 2008

  p  E
Physics 208 Lecture 7
22
Dipole in non-uniform field

A permanent dipole is near a positive point
charge in a viscous fluid. The dipole will
A. rotate CW & move toward charge
B. rotate CW & move away
C. rotate CCW & move toward
+
D. rotate CCW & move away
E. none of the above
Feb. 13, 2008
Physics 208 Lecture 7
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