Transcript PPT

Physics 102: Lecture 09
Currents and Magnetism
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
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
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
Physics 102: Lecture 9, Slide 10
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Torque on Current Loop
It is useful to define normal vector ⊥ to loop
F
F
d
d
a
a
normal
F

normal
f
S
f=0
c
b
F
b
f
B
N
B
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
F
Note torque will align
normal parallel to B
like a magnetic dipole!
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.
Area 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
q
(b) • F
r
v
I
Compare magnitude of 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 15
ACT: Adding Magnetic Fields
Two long wires carry opposite current
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
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
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