Download Currents and Magnetism

Physics 102: Lecture 09
Currents and Magnetism
• Today’s lecture will cover Textbook
Sections 19.6-8
Physics 102: Lecture 9, Slide 1
Force of B-field on Current
• Force on 1 moving charge:
– F = q v B sin(q)
– Out of the page (RHR)
+
v
q
• Force on many moving charges:
– F = (q/t)(vt)B sin(q)
= I L B sin(q)
– Out of the page!
B
+ + + +v
L = vt
Physics 102: Lecture 9, Slide 2
I = q/t
Preflight 9.1, 9.2
A rectangular loop of wire is carrying current as shown. There
is a uniform magnetic field parallel to the sides A-B and C-D.
C
D
B
A
I
B
What is the direction of the force on section A-B of the wire?
force is zero
out of the page
into the page
What is the direction of the force on section B-C of the wire?
force is zero
out of the page
into the page
Physics 102: Lecture 9, Slide 3
Preflight 9.1
A rectangular loop of wire is carrying current as shown. There
is a uniform magnetic field parallel to the sides A-B and C-D.
B
C
D
q
B
I
A
B
I
F=ILBsinq
Here q = 0.
What is the direction of the force on section A-B of the wire?
force is zero
out of the page
into the page
Physics 102: Lecture 9, Slide 4
Preflight 9.2
A rectangular loop of wire is carrying current as shown. There
is a uniform magnetic field parallel to the sides A-B and C-D.
I
C
D
X
F
B
A
I
B
Palm into page.
What is the direction of the force on section B-C of the wire?
force is zero
out of the page
into the page
Physics 102: Lecture 9, Slide 5
Preflight 9.1
A rectangular loop of wire is carrying current as shown. There
is a uniform magnetic field parallel to the sides A-B and C-D.
B
C
D
q
B
I
A
B
I
F=ILBsinq
Here q = 0.
What is the direction of the force on section A-B of the wire?
force is zero
out of the page
into the page
Physics 102: Lecture 9, Slide 6
Preflight 9.2
A rectangular loop of wire is carrying current as shown. There
is a uniform magnetic field parallel to the sides A-B and C-D.
I
C
D
X
F
B
A
I
B
Palm into page.
What is the direction of the force on section B-C of the wire?
force is zero
out of the page
into the page
Physics 102: Lecture 9, Slide 7
Torque on Current Loop in B field
C
D
•
F
X
F
F
B
A
A
I
B
C
D
B
F
The loop will ___________
Look from here
Preflights 9.3, 9.4
Net force on loop is _______.
The net torque is __________!
Physics 102: Lecture 9, Slide 8
Torque on Current Loop in B field
C
D
•
F
X
F
B
F
A
A
I
B
C
D
B
F
The loop will spin in place!
Look from here
Preflights 9.3, 9.4
Net force on loop is zero. But the net torque is not!
Physics 102: Lecture 9, Slide 9
Torque on Current Loop in B field
C
D
•
F
X
F
W
F
B
A
I
A
f
B
L
Force on sections B-C and A-D: F =
Torque on loop is t = 2 x (L/2) F sin(f) =
(length x width = area)
 Torque is
Physics 102: Lecture 9, Slide 10
t=
LW = A !
C
D
B
F
Torque on Current Loop in B field
C
D
•
F
X
F
W
F
B
A
I
A
C
D
f
B
B
L
L/2
L/2
Force on sections B-C and A-D: F = IBW
Torque on loop is t = 2 x (L/2) F sin(f) = ILWB sin(f)
(length x width = area)
 Torque is
Physics 102: Lecture 9, Slide 11
t = I A B sin(f)
LW = A !
F
Torque on Current Loop
Magnitude:
F
t = I A B sinf
Direction:
between normal and B
f
B
F
Torque tries to line up the normal with B!
(when normal lines up with B, f=0, so t=0! )
Even if the loop is not rectangular, as long as it is flat:
t = N I A B sinf.
# of
Physics 102: Lecture 9,loops
Slide 12
(area of
ACT: Torque
B
B
I
(1)
(2)
Compare the torque on loop 1 and 2 which have
identical area, and current.
1) t1 > t2
Physics 102: Lecture 9, Slide 13
2) t1 = t2
3) t1 < t2
ACT: Torque
B
B
I
(1)
(2)
Compare the torque on loop 1 and 2 which have
identical area, and current.
Area points out
of page for both!
1) t1 > t2
2) t1 = t2
3) t1 < t2
f = 90 degrees
Physics 102: Lecture 9, Slide 14
t = I A B sinf
Currents Create B Fields
Magnitude of B a
distance r from
(straight)
0wire:
I
B
2r
B
0  4   10 7 Tm / A
r
•
r = distance from wire
Right-Hand Rule, part deux (partie two??)!
Thumb: along ______
Fingers: curl along _________
Palm:
gives _____
Physics 102: Lecture 9, Slide 15
Here’s a currentcarrying wire.
Current I OUT of
page.
Lines of B
Currents Create B Fields
Magnitude:
0I
B
2r
B
Current I OUT
r
0  4   10 7 Tm / A
•
r = distance from wire
Right-Hand Rule, part deux!
Thumb: along I
Fingers: curl along B field lines
Physics 102: Lecture 9, Slide 16
Lines of B
Right Hand Rule Part 2!
I
wire
Fingers
give
B!
http://www4.ncsu.edu/~rwchabay/emimovies/right-ha.html
Physics 102: Lecture 9, Slide 17
Preflight 9.6
A long straight wire is carrying current from left to
right. Near the wire is a charge q with velocity v
v
v
•
(a)
F
r
(b)
r
• F
I
Compare magnetic force on q in (a) vs. (b)
a) has the larger force
b) has the larger force
c) force is the same for (a) and (b)
Physics 102: Lecture 9, Slide 18
Preflight 9.6
A long straight wire is carrying current from left to
right. Near the wire is a charge q with velocity v
v
v
•
(a)
F
r
B•
(b)
r
• F
I
Compare magnetic force on q in (a) vs. (b)
a) has the larger force
b) has the larger force
c) force is the same for (a) and (b)
0I
same B 
2r
same F  qvB sin q
Physics 102: Lecture 9, Slide 19
θ is angle between v and B
(θ = 90° in both cases)
ACT: Adding Magnetic Fields
Two long wires carry opposite current
x
x
What is the direction of the magnetic field above, and midway
between the two wires carrying current – at the point marked “X”?
1) Left 2) Right
Physics 102: Lecture 9, Slide 20
3) Up
4) Down 5) Zero
ACT: Adding Magnetic Fields
Two long wires carry opposite current
B
x
x
What is the direction of the magnetic field above, and midway
between the two wires carrying current – at the point marked “X”?
1) Left 2) Right
Physics 102: Lecture 9, Slide 21
3) Up
4) Down 5) Zero
Force between current-carrying wires
I towards
us
•
B
•
Another I towards us
Conclusion: Currents in same direction ____________!
I towards
us
•
B

Another I away from us
Conclusion: Currents in opposite direction ____________!
Note: this is different from the Coulomb force between like or unlike charges.
Physics 102: Lecture 9, Slide 22
Force between current-carrying wires
I towards
us
•
B
•
F
Another I towards us
Conclusion: Currents in same direction attract!
I towards
us
•
B
 F
Another I away from us
Conclusion: Currents in opposite direction repel!
Note: this is different from the Coulomb force between like or unlike charges.
Physics 102: Lecture 9, Slide 23
Comparison:
Electric Field vs. Magnetic Field
Source
Acts on
Force
Direction
Electric
Magnetic
Charges
Charges
F = Eq
Parallel E
Moving Charges
Moving Charges
F = q v B sin(q)
Perpendicular to v,B
Charges Attract
Currents Repel
Field Lines
Opposites
Physics 102: Lecture 9, Slide 24
B Field Inside Solenoids
Magnitude of Field anywhere inside of solenoid :
n is the number of turns of
wire/meter on solenoid.
B=0 n I
0 = 4 x10-7 T m /A
(Note: N is the total number of turns, n = N / L)
Right-Hand Rule gives Direction:
Thumb - along I
Fingers – curl into interior of solenoid
Palm – gives B
Magnetic field lines look like bar magnet!
Physics 102: Lecture 9, Slide 25
Solenoid has N and S poles!
B Field Inside Solenoids
Magnitude of Field anywhere inside of solenoid :
n is the number of turns of
wire/meter on solenoid.
B=0 n I
0 = 4 x10-7 T m /A
(Note: N is the total number of turns, n = N / L)
Right-Hand Rule gives Direction:
Thumb - along I
Fingers – curl into interior of solenoid
Palm – gives B
Magnetic field lines look like bar magnet!
Physics 102: Lecture 9, Slide 26
Solenoid has N and S poles!
Preflight 9.8
What is the direction of the magnetic field produced
by these solenoids?
(1) to the Right
(2) to the Left
ACT: B Field Inside Solenoids
What is the net force between the two solenoids?
(1) Attractive
Physics 102: Lecture 9, Slide 27
(2) Zero
(3) Repulsive
Preflight 9.8
What is the direction of the magnetic field produced
by these solenoids?
(1) to the Right
(2) to the Left
Right Hand Rule!
Physics 102: Lecture 9, Slide 28
ACT: B Field Inside Solenoids
What is the net force between the two solenoids?
(1) Attractive
(2) Zero
(3) Repulsive
Look at field lines, opposites attract.
Look at currents, same direction attract.
Physics 102: Lecture 9, Slide 29
See you next lecture!
• Read Ch. 20.1, 3-4
• Lots of cool demos next class!
Physics 102: Lecture 9, Slide 30