1B Physics schedule Winter 2009. Instructor: D.N. Basov [e-mail]
Week 1:Jan 5 Mon Lecture: Intro, 15.1-15.3 Lecture: Electric Flux & Gausss law University Holiday Lecture: capacitance Lecture: Capacitors with dielectrics, Electric current Lecture: Potential Lecture: capacitor combinations Lecture: Ohms Law Resistivity, Electric power Wed Lecture: The Coulomb law, Lecture: Gauss law/examples Friday Lecture: the Electric field
2: Jan 12 3: Jan 19 4: Jan 26
Quiz 1: chapter 15 Quiz 2: chapter 16 Lecture: Resistors, series parallel
5: Feb 2 6: Feb 9 7: Feb 16 8: Feb 23 9: March 2 10: March 9 Lecture: Kirchhoffs rules University Holiday Lecture: current loop, solenoid Lecture: Faradays law, Lenzs law Lecture: Energy of the magnetic field Lecture: RC circuits Lecture: Magnetism Quiz 4: chapter 19 Lecture Inductance, Inductors Lecture: AC circuits Quiz 3: chapter 17-18 Lecture: torque on current loop, Amperes law Induced EMF Quiz 5: chapter 20 Lecture: discussion of the final exam OH Fri 4-5pm, 6-7pm
HW: Ch15: 1,10,11,13,15,17,20,24,27,28,30,32,36,38,43,46,48 T.A.:A: Zhoushen Huang Ch16: 1,3,5,8,12,15,19,22,23,25,29,31,33,35,43,45,47,49,60 [e-mail] Ch17: 1,3,8,9,11,13,16,19,20,23,31,33,39,45,52,60 Ch18: 1,3,5,7,13,17,21,26,31,33,35, B: Andreas Stergiou, Ch19: 1,3,8,9,11,15,19,22,24,27,29,34,37,38,41,44,47,49,57,61 [e-mail] Ch20: 1,5,8,11,13,16,18,23,25,27,29,31,34,37,39, Quizzes: Final exam: all material in ch 15-21 HW problems, problems in class, more no make up final for any reason 4 best out of 5 Last update: Jan 30, 2009 No make-up quizzes for any reason
Comparison: Electric Field vs. Magnetic Field Electric Magnetic
Source Acts on Force Direction Field Lines Charges Charges F = Eq Parallel E Moving Charges Moving Charges F = q v B sin() Perpendicular to v,B
Opposites
Charges Attract
Currents Repel
B L= I
ll o
19.9 Magnetic field of a current loops and solenoids
B-field in center by Amperes Law L
closed loop
Bll L o I o NI
N=no. of turns in length L
1
Only segment 1 contributes because BllL for other segments =zero
BL o NI B
4 2 3
o NI
L B o nI N n L
i.e. 2 in the picture
Chapter 20.1 Induced EMF and magnetic flux
Electric current gives rise to magnetic fields B
I Can a magnetic field give rise to a current? The answer is yes! Discovered by Michael Faraday.
Michael Faraday 1791-1867
Chapter 20.1 Induced EMF and magnetic flux
B
Moving magnetic fields induce currents
B
Change the strength of B: Induced current
Moving current loop induces currents
v
B
Induced EMF!
Chapter 20.1 Induced EMF and magnetic flux
SI units: weber (Wb)
Fig. 20.2
20.2&20.4 Faradays law of induction
Faradays law: The induced emf, , in a closed wire is equal to the time rate of change of the magnetic flux, B.
An induced emf, , always gives rise to a current whose magnetic field opposes the original change in magnetic flux. Lenzs law
Michael Faraday 1791-1867
Bind
Faradays Law and Lenzs Law both state that a loop of wire will want its magnetic flux to remain constant. Current loop in xy plane, B directed along +z Suppose, B decreases. Induced current will be such that it aids the original B field Ccw current in the xy plane
2. A circular loop with a radius of 0.20 m is placed in a uniform magnetic field B=0.85 T. The normal to the loop makes an angle of 30o with the direction of B. The field increases to 0.95 T what is the change in the magnetic flux through the loop? Change in flux? 30o B=0.85T
B B ' A 'cos ' BA cos
A ' A R2
' 30o
B A cos (B ' B ) R 2 cos30(B ' B ) B (0.2)2 cos30(0.95 0.85) B 1.1x10 2Wb
B=0.95T
8. A circular coil with a radius of 20 cm is in a field of 0.2 T with the plane of the coil perpendicular to the field. If the coil is pulled out of the field in 0.30 s find the average emf during this interval B BA cos 0 N N t t N= 1 B cos= 1 R2 A=
B=0
B R 2 0.2 (0.2)2 0.3 t 8.4 x102V
20.3 Motional emf
A voltage is produced by a conductor moving in a magnetic field Charges in the conductor experience a force upward
x x x x x x x x x x x x x x
F qvB
F
x x x
V
x x
v
The work done in moving a charge from bottom to top
W FL qvBL
L
x
The potential difference is
V W vBL q
B into the page
20.3 Motional emf
A voltage is produced by a conductor moving in a magnetic field Charges in the conductor experience a force upward
x x x x x x x x x x x x x x
V o lt a g e velocity
F qvB
F
x x x
V
x x
v
L
x
W FL qvBL
The potential difference is
V W vBL q
B into the page
20.3 Motional emf
The potential difference can drive a current through a circuit The emf arises from changing flux due to changing area according to Faradays Law wire
x x x x
x AB B V vLB LB t t t
x x x x x x x x x x x
I F
R
x x x
v
L
x x
BLv I R R
V
Changing Magnetic Flux B into the page
V
W vBL q
18. R= 6.0 and L=1.2 m and B=2.5 T. a) What speed should the bar be moving to generate a current of 0.50A in the resistor? b) How much power is dissipated in R? c) Where does the power come from? wire
x x x x
a)
x x x x x x x x x x x x
I F
R
x x x
v
BLv R I R IR 0.5(6.0) v BL 2.5(1.2) v 1.0m / s
P I 2R (0.5)2 (6.0) P 1.5W
V
L
x
b)
B into the page
c) Work is done by the force moving the bar
20.4 Lenzs law revisited
Lenzs Law determines the direction of current flow.
B N t
S N
B
V
I
20.4 Lenzs law revisited
Lenzs Law determines the direction of current flow.
B N t
S N
B
V
20.4 Lenzs law revisited
Lenzs Law The polarity of the induced emf is such that it induces a current whose magnetic field opposes the change in magnetic flux through the loop. i.e. the current flows to maintain the original flux through the loop. B increasing in loop B S N
Bin
change in flux
Bin acts to oppose the
V
I
Current direction that produces Bin is as shown (right hand rule)
20.4 Lenzs law revisited
Now reverse the motion of the magnet The current reverses direction
B decreasing in loop
Bin
S N B
change in flux
Bin acts to oppose the
V
I
Current direction that produces Bin is as shown (right hand rule) Emf has reversed its polarity.
20.4 Lenzs law revisited
Lenzs Law and Reaction Forces Fcm B S N N I Fmc A force is exerted by the magnet on loop to produce the current A force must be exerted by the current on the magnet to oppose the change
Bin
S
V
The current flowing in the direction shown induces a magnetic dipole in the current loop that creates a force in the opposite direction
20.4 Lenzs law revisited
Example. Eddy currents A magnet is dropped down a cylindrical conductor. Currents are induced in the conductor to oppose the movement of the magnet
S N B increasing N I S Bin Induced magnetic field creates magnetic dipole that opposes the movement of magnet
20.4 Lenzs law revisited
Example. Eddy currents What about the region behind the magnet?
S N
N
I
S
Bin creates magnetic dipole that opposes the movement of magnet B decreasing
Flux through a rotating loop in a B field
Normal to the plane B The flux through the loop
20.5 Generators
t
B BA cos
= angular velocity (radians/s)
B
20.5 Generators B Relation between B and t
BA
B
t -BA BA
B BA cos t
B t
-BA
B BA sin t t
t proportional to
20.5 Generators
The emf generated by a loop of N turns rotating at constant angular velocity is
B N t
NBA sin t
NBA
0 t
-NBA
20.5 Generators
The emf generated by a loop of N turns rotating at constant angular velocity is
B N t
NBA sin t
NBA
0 t
ac generator ac: alternating current
-NBA
20.5 Generators
35. In a model ac generator, a 500 turn rectangular coil 8.0 cmx 20 cm rotates at 120 rev/min in a uniform magnetic field of 0.60 T. a) What is the maximum emf induced in the coil?
NBA sin t
The maximum value of
max NBA max
(120 x 2 ) (500)(0.6)(0.08 x 0.2) 60V 60
20.5 Generators
Alternating Current (AC) generator
Rotational Work
20.5 Generators
Direct Current (DC) generator
20.5 Generators
A generator is motor acting in reverse
I drives rotation DC motor
20.6 Self-Inductance
a property of a circuit carrying a current a voltage is induced that opposes the change in current used to make devices called inductors Self- inductance of a circuit a reverse emf is produce by the changing current
B t
20.6 Self-Inductance
Self-inductance of a coil
+ B B increases,
B t
changes magnetic flux in the coil, I Current increasing
B AB t t
B AB N N t t
Produces emf in coil
The direction of the induced emf opposes the change in current.
20.6 Self-Inductance
A changing current in a coil induces an emf that opposes the change + +
I I increasing induced emf opposes I
I
I decreasing induced emf supports I
20.6 Self-Inductance
Inductance L is a measure of the The self-induced emf is self-induced emf
B N t
but
I Current increasing
B I t t
proportionality constant is L
I L t
L is a property of the coil, Units of L , Henry (H)
Vs A
20.6 Self-Inductance
Inductance of a solenoid with N turns and length , wound around an air core (assume the length is much larger than the diameter).
B t
l
A
I t
N B BA o IA B N I o A t t
B N 2 I I o A L N t t t
N2 L o A
inductance proportional to N squared x area/length
20.6 Self-Inductance
An air wound solenoid of 100 turns has a length of 10 cm and a diameter of 1 cm. Find the inductance of the coil. l= 10 cm
I
2
d=1 cm
N N d L o A o 4 2 2 7 4 10 (100) (0.01) 5 L 1.0 x10 H 0.1(4)
2
2
20.7 RL circuits
The inductor prevents the rapid buildup of current But at long time does not reduce the current, I
I L t
I Io (1 e ) L Applications of Inductors: R
Reduce rapid changes of current in circuits Produce high voltages in automobile ignition.
t
t
0
at t=
20.8 Energy stored in a magnetic field
B=0 B increasing Bo
I
I=Io
Work is done against to produce the B field. This produces a change in the PE of the inductor
12 PEL LI 2
This stored PE can be used to do work Energy is stored in a magnetic field of an inductor.
20.7 RL circuits
Spark generation
Vs I Switch
L
I L t
is very high (1000 V) if switch is opened quickly. Used to generate high voltage in spark plugs in automobile ignition
Vs Switch
L +
I decreasing