Download PPT

Physics 102: Lecture 09
Currents and Magnetism
•
•
•
•
Exam 1 Monday night
Conflicts, etc.—see course home page
Be sure to bring your ID and go to correct room
Review Sunday, 3-5 PM, Rm. 141
– I will work through HE1 from last semester (fall ‘10)
– To be most useful, you should work the exam yourself
prior to the review
Physics 102: Lecture 9, Slide 1
Summary of Today
• Last time:
– Magnetic forces on moving charge
• magnitude F = qvBsin()
• direction: right-hand-rule
• Today:
– Magnetic forces on currents and current loops
– Magnetic fields due to currents
• long straight wire
• solenoid
Physics 102: Lecture 9, Slide 2
Force of B-field on Current
• Force on 1 moving charge:
– F = q v B sin()
– Out of the page (RHR)
B
+
v

• Force on many moving charges:
– F = q v B sin()
= (q/t) (vt) B sin()
= I L B sin()
– Out of the page!
Physics 102: Lecture 9, Slide 3
B
+ + + +v
L = vt
I = q/t
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
I
a
b
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
Physics 102: Lecture 9, Slide 4
60%
25%
15%
I
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.
c
d
F
B
I
a
b
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
8%
20%
72%
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 section c-d is zero! Same as a-b
Physics 102: Lecture 9, Slide 6
I
F=IBLsin
Here  = 180°
ACT: 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
F
B
I
a
b
What is the direction of the force on section d-a 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
F
F
B
I
a
a
d
c
b
F
b
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 8
B
Torque on Current Loop
The loop will spin in place!
F
F
a
a
Recall from Phys 101:
𝜏 = 𝐹𝐿 sin 𝜃
F
d

ad
d
c
L
b
c
b
F
bc F
B
B
w
F
F
Force on sections b-c and a-d: F = IBw
Torque on loop is t = L F sin() = I Lw B sin()
 Torque is: 𝜏 = 𝐼𝐴𝐵 sin 𝜃
Physics 102: Lecture 9, Slide 9
Lw = A !
ACT: Torque on Current Loop
What is the torque on the loop below?
1) t < IAB
2) t = IAB
3) t > IAB
t=0
Physics 102: Lecture 9, Slide 10
xxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
Torque on Current Loop
It is useful to define normal vector ⊥ to loop
F
F
d
d
a
a
normal
F
S
c
b
F
b
normal
f
f=0
B
N
f=0
c
F
f = 180 – 
Torque is: 𝜏 = 𝐼𝐴𝐵 sin 𝜃 = 𝐼𝐴𝐵 sin 𝜑
If there are N loops: 𝜏 = 𝑁𝐼𝐴𝐵 sin 𝜑
Even if loop is not rectangular, as long as it is flat
Physics 102: Lecture 9, Slide 11
normal

normal
f
F
B
F
F
Note torque will align
normal parallel to B
like a magnetic dipole!
B
Current loops act like dipoles
Orbits of electrons
“spin”
Electron orbit and “spin” are current loops
Why some materials are magnetic
Nuclear Magnetic Resonance (NMR) and MRI
Physics 102: Lecture 9, Slide 12
ACT: Torque
B
B
I
(1)
(2)
Compare the torque on loop 1 and 2 which have identical
area, and current.
Normal vector points
out of page for both!
1) t1 > t2
2) t1 = t2
3) t1 < t2
f = 90
Physics 102: Lecture 9, Slide 13
t = I A B sin(f)
Currents create magnetic fields
• Straight wire carrying current I generates a field B
at a distance r:
−7
𝜇
=
4𝜋
×
10
𝑇𝑚/𝐴
0
𝜇 𝐼
𝐵=
0
2𝜋𝑟
• “Right-hand rule 2”:
– Thumb of right hand along I
– Fingers of right hand along r
– Out-of-palm points along B
“Permeability of free space”
(similar to e0 for electricity)
B
r
I (out of page)
B field circles wire
Physics 102: Lecture 9, Slide 14
Note: there are different versions of RHR
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
q
•
(a)
F
v
r
B
q
(b) • F
r
v
I
Compare magnitude of magnetic force on q in (a) vs. (b)
34%
a) has the larger force
50%
b) has the larger force
c) force is the same for (a) and (b) 16%
𝜇0 𝐼
Same 𝐵 =
2𝜋𝑟
Physics 102: Lecture 9, Slide 15
Same 𝐹 = 𝑞𝑣𝐵 sin 𝜃
 = 90 for (a) and (b)!
Same magnitude
Different directions
ACT: Adding Magnetic Fields
Two long wires carry opposite current
B
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 16
3) Up
4) Down 5) Zero
Force between current-carrying wires
Currents in same direction
B
F
I towards us
Another I towards us
Currents in same
direction attract!
Physics 102: Lecture 9, Slide 17
Currents opposite direction
B
F
I towards us
Another I away from us
Currents in opposite
direction repel!
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
Field Lines
+
Opposites
Physics 102: Lecture 9, Slide 18
Charges Attract
Currents Repel
ACT: Force between Wires
What is the direction of the force on
the top wire, due to the two below?
1) Left
Physics 102: Lecture 9, Slide 19
2) Right
3) Up
4) Down 5) Zero
Solenoids
• A solenoid consists of N loops of wire
B is uniform everywhere inside of solenoid:
𝜇0 = 4𝜋 × 10−7 𝑇𝑚/𝐴
𝐵 = 𝜇0 𝑛𝐼
n is the number of turns of wire/meter (n = N/L)
• Use “Right-hand rule 2”
B
N
S
B
I
I
Physics 102: Lecture 9, Slide 20
B field lines look like bar magnet!
Solenoid has N and S poles!
ACT: The force between the two
solenoids is …
(1) Attractive
(2) Zero
(3) Repulsive
Look at field lines, opposites attract.
Look at currents, same direction attract.
Physics 102: Lecture 9, Slide 21
Summary of Right-Hand Rules
RHR 1
RHR 2
Force on moving q
Alternate
B field from current I
Straight wire
I
B
r
I
Solenoid
B
I
Physics 102: Lecture 9, Slide 22