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Sep. 23, 2008 Physics 208 Lecture 7 1
From last time…
Electric field lines
Electric fields
AB
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Sep. 23, 2008 Physics 208 Lecture 7 2
Exam 1 Mon. Sep. 29, 5:30-7 pm, 2103 Ch (here)
Covers Chap. 21.5-7, 22, 23.1-4, 23.7, 24.1-5, 26-27 + lecture, lab, discussion, HW
Review Group/Quiz (solutions on website).Review lab question sheets. Review sample exams on website.
Students with scheduled class conflicts: stay after lecture today to arrange alt. exam time
8 1/2 x 11 handwritten note sheet (both sides) allowed
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Sep. 23, 2008 Physics 208 Lecture 7 3
Electric field lines Local electric field tangent to
field line Density of lines proportional to
electric field strength Fields lines can only start on +
charge Can only end on - charge. Electric field lines can never
cross
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Sep. 23, 2008 Physics 208 Lecture 7 4
QuestionHow are the charges A and B related?
A) A+, B-,
B) A-, B+,
C) A+, B-,
D) A-, B+,
E) A+, B-,
€
A < B
€
A < B
€
A > B
€
A < B
€
A = B
AB
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Sep. 23, 2008 Physics 208 Lecture 7 5
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
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Sep. 23, 2008 Physics 208 Lecture 7 6
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?
+ + + + + + + + + + + + + + + + + + +
xA.
B. C.
D.
E.
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Sep. 23, 2008 Physics 208 Lecture 7 7
E-field: infinite line of charge
Charge density Coulombs/meter
y
+ + + + + + + + + + + + + + + + + + + +
€
dQ = λdx
€
dr E
r
x€
r2 + x 2€
θ
€
dEy = cosθdE
= 14πεo
dQ
r2 + x 2( )
2 cosθ
= 14πεo
dQr2 + x 2
rr2 + x 2
= 14πεo
rλdx
r2 + x 2( )3 / 2
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Sep. 23, 2008 Physics 208 Lecture 7 8
Add all these up
Units?€
Ey = 2 14πεo
rλdx
r2 + x 2( )3 / 2
0
∞
∫
= λ2πεo
xdx
r r2 + x 2( )1/ 2
0
∞
=
€
2πεor
€
=2k λr
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Sep. 23, 2008 Physics 208 Lecture 7 9
Finite line of charge
What direction is the E-field above the end of the line charge?
+ + + + + + + + + + + + + + + + + + + +
A
B
CD
E
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Sep. 23, 2008 Physics 208 Lecture 7 10
Ring of uniform positive chargeWhich is the graph of the
field on the axis? y
x
z
A)
B)
C)
D)
E)
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Sep. 23, 2008 Physics 208 Lecture 7 11
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
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Sep. 23, 2008 Physics 208 Lecture 7 12
E-field of plane of charge
Text does this as adding up rings of charge.
€
E plane = η2εo
€
η =Surface charge density
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Sep. 23, 2008 Physics 208 Lecture 7 13
Electric fields and forces
Original definite of E-field was(Coulomb Force) / charge
E-field produced force on charged particle.
€
F = q
r E
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Sep. 23, 2008 Physics 208 Lecture 7 14
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
Quick Quiz
FeA negative charge in outer space is in a uniform E-field that points to the right. What is the motion of the particle?
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Sep. 23, 2008 Physics 208 Lecture 7 15
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
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Sep. 23, 2008 Physics 208 Lecture 7 16
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
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Sep. 23, 2008 Physics 208 Lecture 7 17
A. Accel left continuously
B. Accel left, then moves at const. speed
C. Accel left, then slows to stop
D. Accel left, then turns around
E. None of the above
Quick QuizA negative charge is released in a fluid with a uniform E-field that points to the right. The fluid imparts a force proportional to and opposite to the velocity
What is the motion of the particle?
Uniform E
Fe Fluid
€
F fluid = −b
r v
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Sep. 23, 2008 Physics 208 Lecture 7 18
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
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Sep. 23, 2008 Physics 208 Lecture 7 19
Application: Gel Electrophoresis Charged macromolecules in ‘gel’ with applied E-field Electric force: FE = qE
Drag force: FD ~ -cv v = qE / c Speed depends on
charge and drag (molecule size) Sometimes too complex to interpret Protein electrophoresis:
soak in detergent to give proteinsall the same charge density.
Result, small proteins move faster
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Steady state: FE+FD=0
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Sep. 23, 2008 Physics 208 Lecture 7 20
Quick Quiz
An electric dipole is in a uniform electric field as shown. The dipole
DipoleA. accelerates left
B. accelerates right
C. stays fixed
D. accelerates up
E. none of the above
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Sep. 23, 2008 Physics 208 Lecture 7 21
Electric torque on dipoles
Total torque has magnitude
€
τ =
r ×
r F ,
magnitude rF sinθ
€
F+ = qE, r = s /2F− = −qE, r = s /2
€
r +
€
r −
€
τ =qsE sinθ
Dipole moment has magnitude
€
p = qs
€
τ =
p ×
r E
Torque on dipole in uniform field
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Sep. 23, 2008 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
+