Transcript Currents and Magnetism

Physics 102: Lecture 09
Currents and Magnetism
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Exam 1 Monday night
Conflicts, etc.—see course home page
Be sure to bring your ID and go to correct room
Review Sunday, 3-4:30 PM, rm. 141
– I will work through HE1 from Fall 2007
– To be most useful, you should work the exam
yourself prior to the review
Summary of Today
• Last time
– Magnetic field lines
– Magnetic forces on moving charge
• magnitude F=qvBsin()
• direction: right-hand-rule
• Magnetic forces on currents and current
loops
• Magnetic fields due to currents
– long straight wire
– solenoid
Force of B-field on Current
• Force on 1 moving charge:
– F = q v B sin()
– Out of the page (RHR)
+
v

• Force on many moving charges:
– F = (q/t)(vt)B sin()
= I L B sin()
– Out of the page!
B
+ + + +v
I = q/t
L = vt
Demo: 184
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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

B
a
I
b
I
F=IBLsin
Here  = 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
demo 253
46%
36%
18%
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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
13%
29%
58%
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Force on Loop
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

B
a
I
b
Force on C-D is Zero!
I
F=IBLsin
Here  = 180º
I
B
same as for A-B!
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Force on Loop (cont’d)
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
F
I
•
F
Palm out of page.
Force on A-D is out of the page.
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Torque on Current Loop in B field
c
d
•
F
X
F
B
F
a
a
I
c
d
b
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!
“As long as the net force on the loop is zero, there is no reason for the loop to move.”
demo 68
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Torque on Current Loop in B field
c
d
•
F
X
F
W
F
B
a
I
a
c
d
f
b
F
b
L
Force on sections B-C and A-D: F = IBW
Torque on loop is t = L F sin(f) = ILWB sin(f)
(length x width = area)
 Torque is
LW = A !
t = I A B sin(f)
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ACT: Torque on Current Loop
What is the torque on the loop below?
1) t < IAB
2) t = IAB
3) t > IAB
t=0
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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
loops
(area of
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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
t = I A B sinf
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Currents Create B Fields
Magnitude:
0I
B
2r
B
Current I OUT
r
0  4   10 7 Tm / A
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r = distance from wire
Right-Hand Rule, part deux!
Thumb:
Fingers:
Palm:
Lines of B
on I
position you want to know B at
gives B
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Right Hand Rule Part 2!
I
wire
Fingers
give
B!
http://www4.ncsu.edu/~rwchabay/emimovies/right-ha.html
ACT/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)
33%
a) has the larger force
51%
b) has the larger force
c) force is the same for (a) and (b) 16%
0I
same B 
2r
same F  qvB sin 
Different directions
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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
3) Up
4) Down 5) Zero
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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!
demo 740
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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()
Perpendicular to v,B
Charges Attract
Currents Repel
Field Lines
Opposites
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ACT: Force between Wires
What is the direction of the force on
the top wire, due to the two below?
1) Left 2) Right
3) Up
4) Down 5) Zero
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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)
Another Right-Hand Rule gives Direction:
Curl fingers in direction of current
Thumb point in direction of B
Magnetic field lines look like bar magnet!
demo 183
Solenoid has N and S poles!
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ACT: B Field Inside Solenoids
(1) Attractive
(2) Zero
(3) Repulsive
Look at field lines, opposites attract.
Look at currents, same direction attract.
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See you Monday!
• Lots of cool demos!
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