I2
Last time…
Equivalent resistance
(parallel, series)
Exam 2 is
Kirchoff’s
junction law
I1
I3
I1 =I2 +I3
I1
ε
Tuesday Oct. 28
5:30-7 pm, 2103 Ch (here)
Students w / scheduled academic conflict please stay
after class Tues. Oct. 21 to arrange alternate time.
R1
R2
I2
Covers: all material since exam 2.
Bring: Calculator
R3
I3
One (double-sided) 8 1/2 x 11 note sheet
Exam review: Thursday, Oct. 23, in class
Kirchoff’s loop law
Thur. Oct. 16, 2008
Physics 208 Lecture 14
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Thur. Oct. 16, 2008
Resistorcapacitor circuit



Physics 208 Lecture 14
Discharging the capacitor
What happens to charges on
the capacitor after switch is
closed?
Kirchoff’s loop law

(VB " VA ) + (VD " VC ) = 0
Why does the charge flow
through the resistor?
"Vc = Qc /C
"IR
!
!
C
A
D
Charges in the current I come from capacitor:
I="
!
Physics 208 Lecture 14
B
Q
"I= c
RC
!
Why does the charge on the
capacitor change in time?
Thur. Oct. 16, 2008
2
3
Thur. Oct. 16, 2008
dQc
dt
Physics 208 Lecture 14
4
!
Charging a capacitor
RC discharge

Again
Kirchoff’s loop law:
" # IR # Q /C = 0
" I = # /R $ Q
C

C
RC time constant
!
" = RC
Thur. Oct. 16, 2008
!
t increases: Qc > 0 " I < # /R
Looks like resistor & battery:
uncharged cap acts like short circuit
VC increases, so V R decreases
!
Time t = ∞: VC = " # VR = 0 # I = 0
I = Ioe"t / #
!
Time t = 0: Qc = 0 " I = # /R
!
Q = Qoe"t / #
/RC
Physics 208 Lecture 14
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!
Thur. Oct. 16, 2008
Fully charged capacitor acts
like open circuit
Physics 208 Lecture 14
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!
!
1
Discharging a capacitor
Question
The circuit contains three identical light
bulbs and a fully-charged capacitor.
Which is brightest?
A. A
B. B
Q = Qmax (1" e"t / # )
C. C
D. A & B
E. All equally bright
!
Thur. Oct. 16, 2008
Physics 208 Lecture 14
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Thur. Oct. 16, 2008
Physics 208 Lecture 14
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Human capacitors
Question

The circuit contains three identical light
bulbs and an uncharged capacitor.
Which is brightest?
Cell membrane:

100 µm


A. A
‘Empty space’ separating
charged fluids (conductors)
~ 7 - 8 nm thick
In combination w/fluids, acts as
parallel-plate capacitor
B. B
Extracellular fluid
C. C
Plasma membrane
D. A & B
E. All equally bright
Thur. Oct. 16, 2008
Cytoplasm
Physics 208 Lecture 14
9
Cell Membrane
RC circuit
Thur. Oct. 16, 2008
Physics 208 Lecture 14
10
Magnetism
Nerve signal is an action
potential that propagates down
RC cell-membrane network
Thur. Oct. 16, 2008
Physics 208 Lecture 14
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Thur. Oct. 16, 2008
Physics 208 Lecture 14
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2
Magnets and magnetic fields
Magnetic dipoles

Magnetic charges (monopoles) have never been
observed.


Magnetic dipole characterized by dipole moment
r r r
Torque on magnetic dipole " = µ # B
r r r
( Compare electric dipole: " = p # E )
r
µ
!
!
!
Torque tends to aligns magnetic
dipole with magnetic field
Thur. Oct. 16, 2008
Physics 208 Lecture 14
13
Thur. Oct. 16, 2008
Magnets
Clearly magnets interact with each other

Sometimes attracting, sometimes repelling



But the magnetic particles are sort of a ‘composite’
positive and negative ‘magnetic charge’.
These ‘magnetic charges’ cannot be broken apart —
always appear in N-S pairs.
Thur. Oct. 16, 2008
N
Physics 208 Lecture 14
15
Magnetic field

Similar in spirit to electric field

Exerts torque on a mangetic dipole



North Pole and
South Pole
 Are inseparable
Visualized as a bar with positive pole (North) at one
end and negative pole (South) at other.
S

14
Let’s Break A Magnet!


Physics 208 Lecture 14
16
N
• Magnetic Field Lines
– Arrows give direction
– Density gives strength
– Looks like dipole
Aligns it with magnetic field lines.
Magnetic field lines indicate
direction of local magnetic field
S

leave magnet at N pole

enter magnet at S pole
Thur. Oct. 16, 2008
Physics 208 Lecture 14
Magnetic Field Lines
Magnetic field exerts a torque on
compass needle
Field lines
Thur. Oct. 16, 2008
Physics 208 Lecture 14
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17
Thur. Oct. 16, 2008
Physics 208 Lecture 14
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18
3
Electric vs Magnetic Field Lines





Leave +, North
Enter -, South

Differences




Density gives strength
Arrow gives direction


Magnetism: Permanent magnets
Similarities
Start/Stop on electric charge
No Magnetic Charge, lines are continuous!

Convention for 3-D situations:


Physics 208 Lecture 14
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N
Called magnetic dipole
(North pole
and South pole)
S
S
Poles interact with each other
similar to charges.
Thur. Oct. 16, 2008
Likes repel
N
This is the elementary
magnetic particle
x x x x x x x INTO Page
••••••••••••• OUT of Page
Thur. Oct. 16, 2008
Opposites
attract
North Pole
and South Pole
N
S
S
N
Physics 208 Lecture 14
20
The Earth is a magnet
Earth is a bar
magnet.
North magnetic
pole ~ at south
geographic pole
A compass is a
bar magnet
Compass needle aligns
with local Earth field
Thur. Oct. 16, 2008
Physics 208 Lecture 14
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4