# Last time… ε Exam 2 is Tuesday Oct. 27 5:30 ```I2
Last time…
Exam 2 is
Kirchoff’s
junction law
I1
Equivalent resistance
(parallel, series)
I3
I1=I2+I3
I1
ε
Tuesday Oct. 27
5:30-7 pm, 145 Birge
after class Tues. Oct. 20 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. 22, in class
Kirchoff’s loop law
Thur. Oct. 15, 2009
Physics 208 Lecture 13
1
Thur. Oct. 15, 2009
Charging a capacitor

The circuit contains three identical light
bulbs and a fully-charged capacitor.
Which is brightest?
C
C
€
/RC
Time t = 0: Qc = 0 ⇒ I = ε /R
€
t increases: Qc &gt; 0 ⇒ I &lt; ε /R
Thur. Oct. 15, 2009
A.  A
Looks like resistor &amp; battery:
uncharged cap acts like short circuit
B.  B
C.  C
VC increases, so VR decreases
€
Time t = ∞: VC = ε ⇒ VR = 0 ⇒ I = 0
€
2
Question
Again
Kirchoff’s loop law:
ε − IR − Q /C = 0
⇒ I = ε /R − Q
Physics 208 Lecture 13
D.  A &amp; B
Fully charged capacitor acts
like open circuit
Physics 208 Lecture 13
E.  All equally bright
3
Thur. Oct. 15, 2009
Physics 208 Lecture 13
4
€
Discharging the capacitor
Question
The circuit contains three identical light
bulbs and an uncharged capacitor.
Which is brightest?

Kirchoff’s loop law
(VB − VA ) + (VD − VC ) = 0
ΔVc = Qc /C
A.  A
€
B.  B
C
A
D
Q
⇒I= c
RC
Charges in the current I come from capacitor:
D.  A &amp; B
E.  All equally bright
Thur. Oct. 15, 2009
€
€
C.  C
−IR
B
I=−
€
Physics 208 Lecture 13
5
Thur. Oct. 15, 2009
Physics 208 Lecture 13
dQc
dt
6
€
1
RC discharge

Charging a capacitor
RC time constant
τ = RC
Q = Qoe
Q = Qmax (1− e−t / τ )
−t / τ
I = Ioe−t / τ
€
Thur. Oct. 15, 2009
€
Physics 208 Lecture 13
7
Thur. Oct. 15, 2009
Physics 208 Lecture 13
8
€
€
Cell Membrane
RC circuit
Human capacitors

Cell membrane:

100 &micro;m


‘Empty space’ separating
charged fluids (conductors)
~ 7 - 8 nm thick
In combination w/fluids, acts as
parallel-plate capacitor
Extracellular fluid
Nerve signal is an action
potential that propagates down
RC cell-membrane network
Plasma membrane
Cytoplasm
Thur. Oct. 15, 2009
Physics 208 Lecture 13
9
Thur. Oct. 15, 2009
Magnetism
Physics 208 Lecture 13
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’.
Visualized as a bar with positive pole (North) at one
end and negative pole (South) at other.
These ‘magnetic charges’ cannot be broken apart —
always appear in N-S pairs.
S
Thur. Oct. 15, 2009
Physics 208 Lecture 13
10
11
Thur. Oct. 15, 2009
N
Physics 208 Lecture 13
12
2
Magnetic field
Let’s Break A Magnet!

Similar in spirit to electric field

Exerts torque on a mangetic dipole
North Pole and
South Pole
  Are inseparable



13
Opposites
attract
This is the elementary
magnetic particle

Thur. Oct. 15, 2009


Physics 208 Lecture 13
14
But really one of the magnets is trying to align the other one.
N
N
N
S
N
N
S
S
S
S
N
S
S
N
Physics 208 Lecture 13
A
15
N
S
S
B
Thur. Oct. 15, 2009
N
N
S
S
C
D
Physics 208 Lecture 13
16
Magnetic Field Lines
Magnetic charges (monopoles) have never been
observed.

enter magnet at S pole
Which way will these magnets tend to align?
N
Magnetic dipoles


S
Poles interact with each other
similar to charges.

leave magnet at N pole
Alignment force
Likes repel
N
Called magnetic dipole
(North pole
and South pole)

S

Thur. Oct. 15, 2009
Magnetism: Permanent magnets
North Pole
and South Pole

Aligns it with magnetic field lines.
Field lines

Physics 208 Lecture 13
Magnetic field exerts a torque on
compass needle
Magnetic field lines indicate
direction of local magnetic field

Thur. Oct. 15, 2009
N
Magnetic dipole characterized by dipole moment
  
Torque on magnetic dipole τ = &micro; &times; B
  
( Compare electric dipole: τ = p &times; E )
€

&micro;
€
•  Magnetic Field Lines
–  Arrows give direction
–  Density gives strength
–  Looks like dipole
-
€
Torque tends to aligns magnetic
dipole with magnetic field
Thur. Oct. 15, 2009
Physics 208 Lecture 13
S
17
Thur. Oct. 15, 2009
Physics 208 Lecture 13
N
+
18
3
Magnets and magnetic fields
Electric vs Magnetic Field Lines

Similarities


Density gives strength
Arrow gives direction



Differences



Leave +, North
Enter -, South
Start/Stop on electric charge
No Magnetic Charge, lines are continuous!
Convention for 3-D situations:


x x x x x x x INTO Page
••••••••••••• OUT of Page
Thur. Oct. 15, 2009
Physics 208 Lecture 13
19
Thur. Oct. 15, 2009
Definition of Magnetic Field
Physics 208 Lecture 13
Magnetic force
on moving
charged particle
Defined electric field based on electric force on a
charged particle.
Is there a magnetic force on charged particle?

S
Observation:

Magnetic field has no effect on stationary charged particle

Empirical facts: a) magnitude: ∝ to velocity of q
q
v
Tue. Oct. 21, 2008
Physics 208 Lecture 15
21


Charged particle not moving

Physics 208 Lecture 15
22
Magnitude of force is proportional to

no effect

Charged particle is moving:

b) direction: ⊥ to direction of q
Magnetic force on charged particle
Effect of uniform B-field on charged particle

F mag
Tue. Oct. 21, 2008
Magnetic force on electric charges

20

force exerted perpendicular
to both field and
velocity

Charge of particle, q
Speed of particle, v
Strength of magnet field, B


sin(θ), θ=angle between B and v
FB = q vB sin θ
Direction of force is perpendicular
€ to both
€


B and v

 
F = qv &times; B
€
Tue. Oct. 21, 2008
Physics 208 Lecture 15
23
vector ‘cross product’
€
Tue. Oct. 21, 2008
Physics 208 Lecture 15
€
24
€
4
FB on a Charge Moving in a
Magnetic Field, Formula
Quick Quiz
The three charges below have equal charge and speed,
but are traveling in different directions in a uniform
magnetic field.
FB = q v x B




FB is the magnetic force
q is the charge
v is the velocity of the
moving charge
B is the magnetic field
Which particle experiences the greatest magnetic force?
B
A.  1
B.  2
3

SI unit of magnetic field: tesla (T)
T=

C.  3
N
N
=
C ⋅ m /s A ⋅ m
2
104
1
CGS unit: gauss (G): 1 T =
Tue. Oct. 21, 2008
G (Earth surface 0.5 G)
Physics 208 Lecture 15
25
D.  All same
F = q v B sin(θ)
Tue. Oct. 21, 2008
Physics 208 Lecture 15
26
€
Quick Quiz
Force on moving charged particle

 
F = qv &times; B
The three charges below have equal charge and speed,
but are traveling in different directions in a uniform
magnetic field.
The force on all the particles is in the same direction.
B
3
2
1
Tue. Oct. 21, 2008
€
A.  True
B.  False

F =0
Magnitude F = q v B sin(θ)

F intermediate

F is max
All forces are into page
Physics 208 Lecture 15
27
€
Tue. Oct. 21, 2008
€
€
Physics 208 Lecture 15
28
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