B - Purdue Physics
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Transcript B - Purdue Physics
Question
The bar magnet produces a magnetic field at the compass location
Whose strength is comparable to that of the Earth. The needle of the
compass points in what direction?
A)
A
B)
B
C)
D)
C
E)
D
E
N
Compass
S
Bearth
N
The Magnetic Field of a Bar Magnet
How does the magnetic field around a bar magnet look like?
N
S
Clicker: Frame with conventional current is introduced into the B
field of horseshoe magnet.
Frame will
S
A. Stay as it was put in
I
On the axis perpendicular to the B
field rotate clockwise
B. 90 degree
N Towards you
C. 180 degree
D. 270 degree
Modern Theory of Magnets
2. Spin
Electron acts like spinning charge
- contributes to
Electron spin contribution to is of the same order as one due to
orbital momentum
Neutrons and proton in nucleus also have spin but their ‘s are
much smaller than for electron (can be ignored in modeling bar
magnet)
same angular momentum: 1 e
2m
NMR, MRI – use nuclear
Nuclear Magnetic Resonance
Proton spin
Magnet
N
S
Felix Bloch
(1905 -1983)
Edward Purcell
(1912-1997)
B field
Electron Spin Resonance (ESR)
B field
Magnetic Resonance Imaging
B
Clicker
What is the direction of the magnetic
field inside the solenoid?
Current upward on
side nearest you
A.
B.
C.
D.
Magnetic Field of a Solenoid
Step 1: Cut up the distribution
into pieces
Step 2: Contribution of one piece
origin: center of the solenoid
0
2 R 2 I
one loop: Bz
4 R 2 d z 2
3/2
B
Number of loops per meter: N/L
Number of loops in z: (N/L) z
0
2 R 2 I
Field due to z: Bz
4 R 2 d z 2
3/2
N
z
L
Magnetic Field of a Solenoid
Step 3: Add up the contribution
of all the pieces
0
2 R 2 I
dBz
4 R 2 d z 2
3/2
N
dz
L
0 2 R NI
dz
Bz
2
2
4
L
L /2 R d z
2
L /2
3/2
B
Magnetic field of a solenoid:
0 2 NI
Bz
4 L
2
2
2
2
d
L
/
2
R
d
L
/
2
R
dL/2
dL/2
Magnetic Field of a Solenoid
0 2 NI
Bz
4 L
2
2
2
2
d
L
/
2
R
d
L
/
2
R
dL/2
dL/2
Special case: R<<L, center of the solenoid:
0 2 NI L / 2
L / 2 0 2 NI
Bz
2
2
2
4 L L / 2
4 L
L
/
2
Bz
0 NI
L
in the middle of a long solenoid
Chapter 19
A Microscopic View
of Electric Circuits
Current in a Circuit
A microscopic view of electric circuits:
• Are charges used up in a circuit?
• How is it possible to create and maintain a nonzero electric
field inside a wire?
• What is the role of the battery in a circuit?
In an electric circuit the system does not reach equilibrium!
Steady state and static equilibrium
Static equilibrium:
• no charges are moving
Steady state (Dynamic Equilibrium):
• charges are moving
• their velocities at any location do not change with time
• no build up of charge anywhere
Current in Different Parts of a Circuit
What happens to the charges that flow
through the circuit?
Is the current the same in all parts of a
series circuit? What would be IA
compared to IB?
IB = I A
Test:
1. Can use compass needle deflection for wire A and B
2. Run wires A and B together above compass
A
B
Current in Different Parts of a Circuit
IB = IA in a steady
state circuit
We cannot get something for nothing!
What is used up in the light bulb?
Energy is transformed from one form to another
Electric field – accelerates electron
Friction – energy is lost to heat
Battery – chemical energy is used up
Closed circuit – energy losses to heat and light
Current at a Node
The current node rule
(Kirchhoff node or junction rule [law #1]):
i1 = i 2
i2 = i3 + i 4
In the steady state, the electron current entering a node in a
circuit is equal to the electron current leaving that node
(consequence of conservation of charge)
Gustav Robert Kirchhoff
(1824 - 1887)
Question
Pick right statement:
A) i1 = i4 and i2 = i3
B) i1 i4
C) i1 = i4 and i1= i2+i3
Question
Write the node equation for this circuit.
What is the value of I2?
A)
B)
C)
D)
1A
2A
3A
4A
Exercise
Write the node equation for this circuit.
What is the value of I2?
I1 + I4 = I 2 + I 3
I2 = I1 + I4 - I3 = 3A
What is the value of I2 if I4 is 1A?
I1 + I 4 = I 2 + I 3
I2 = I1 + I4 - I3 = -2A
1A
Charge conservation:
Ii > 0 for incoming
å Ii = 0 Ii < 0 for outgoing
i
Motion of Electrons in a Wire
In a current-carrying wire there must be an electric field to drive the
sea of mobile charges.
What is the relationship between the electric field and the current?
Why is an electric field required?
Interaction between electrons and lattice of atomic cores in metal.
Electrons lose energy to the lattice. Electric field must be present to
increase the momentum of the mobile electrons.
The Drude Model
eE Dt
Average ‘drift’ speed: v =
me
Dt - average time between
collisions
For constant temperature v ~ E
v = uE ,
e
u=
Dt
me
u – mobility of an electron
Electron current: i = nAv
i = nAuE
Paul Drude
(1863 - 1906)
Typical Mobile Electron Drift Speed
Typical electron current in a circuit is ~ 1018 electrons/s.
What is the drift speed of an electron in a 1 mm thick copper
wire of circular cross section?
# electrons
= nAv
s
n » 8.4 ´ 1028 m-3
3.14 × (1 ´ 10 m )
pD
A=
»
= 8 ´ 10 -7 m 2
4
4
-3
2
2
1018 s-1
1018 s-1
-5
v=
»
=
1.5
´
10
m/s
28
-3
-7
2
nA
8.4 ´ 10 m 8 ´ 10 m
(
)(
)
Typical Mobile Electron Drift Speed
Typical electron current in a circuit is 1018 electrons/s.
What is the drift speed of an electron in a 1 mm thick copper
wire? n » 8.4 ´ 1028 m-3
v = 1.5 ´ 10-5 m/s
How much time would it take for a particular electron to move
through a piece of wire 30 cm long?
s
0.3 m
4
t= =
=
2
´
10
s » 5.5 hours!
-5
v 1.5 ´ 10 m/s
How can a lamp light up as soon as you turn it on?
Typical E in a Wire
Drift speed in a copper wire in a typical circuit is 5.10-5 m/s.
The mobility is u=4.5.10-3 (m/s)/(N/C). Calculate E.
v = uE
v
5 ´ 10 -5 m/s
-2
E= =
=
1.1
´
10
N/C
-3
u 4.5 ´ 10 (m/s)/(N/C)
Electric field in a wire in a typical circuit is very small
E and Drift Speed
In steady state current is the same everywhere in a series circuit.
Ethin
Ethick
i
i
What is the drift speed?
i = nAv
nAthin vthin = nAthick vthick
vthin
Athick
=
vthick
Athin
Note: density of electrons n cannot change if same metal
What is E?
v = uE
uEthin
Athick
=
uEthick
Athin
Ethin
Athick
=
Ethick
Athin