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Physics 102: Lecture 9, Slide 1Physics 102: Lecture 9, Slide 1
Currents and Magnetism
Physics 102: Lecture 09
Physics 102: Lecture 9, Slide 2Physics 102: Lecture 9, Slide 2
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 3Physics 102: Lecture 9, Slide 3
Force of B-field on Current
+ v
• Force on 1 moving charge:– F = q v B sin()– Out of the page (RHR)
• Force on many moving charges:– F = q v B sin()
= (q/t) (vt) B sin()
= I L B sin()
– Out of the page!
v
L = vt
B
I = q/t+ + ++
B
Physics 102: Lecture 9, Slide 4
force is zero out of the page into the page
B
I
L
F=IBLsin
Here = 0a b
cd
B
I
Preflight 9.1A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides a-b and c-d.
What is the direction of the force on section a-b of the wire?
Physics 102: Lecture 9, Slide 5
force is zero out of the page into the page
a b
cd
B
I
Preflight 9.2A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides a-b and c-d.
What is the direction of the force on section b-c of the wire?
F
Physics 102: Lecture 9, Slide 6
B
I
L
F=IBLsin
Here = 180°a b
cd
B
I
Force on loopA rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides a-b and c-d.
Force on section c-d is zero! Same as a-b
Physics 102: Lecture 9, Slide 7
force is zero out of the page into the page
a b
cd
B
I
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.
What is the direction of the force on section d-a of the wire?
F
Physics 102: Lecture 9, Slide 8
Net force on loop is zero.Look from here
But the net torque is not!
Torque on Current Loop in B field
The loop will spin in place!
Preflights 9.3, 9.4:
a b
cd
B
I
F F
a b
cd
F
F
B
Physics 102: Lecture 9, Slide 9
Torque on Current LoopThe loop will spin in place!
a b
cd
F
F
Ba
bc
d
F
F
B
a
b
c
d
F
F
B
𝜏= 𝐹𝐿sin𝜃 Recall from Phys 101:
B
F
F
Torque on loop is = L F sin() = I Lw B sin() Force on sections b-c and a-d: F = IBw
𝜏= 𝐼𝐴𝐵sin𝜃 Torque is:
Lw = A !
L
w
Physics 102: Lecture 9, Slide 10Physics 102: Lecture 9, Slide 10
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
ACT: Torque on Current Loop
What is the torque on the loop below?
1) < IAB
2) = IAB
3) > IAB
Physics 102: Lecture 9, Slide 11
Torque on Current LoopIt is useful to define normal vector ⊥ to loop
a
b
c
d
F
F
BB
F
F
𝜏= 𝐼𝐴𝐵sin𝜃 Torque is:
normal
normal
= 180 –
𝜏= 𝑁𝐼𝐴𝐵sin𝜑 If there are N loops:
= 𝐼𝐴𝐵sin𝜑 Note torque will align normal parallel to B like a magnetic dipole!Even if loop is not rectangular, as long as it is flat
a
b
c
d
F
F
B
normal
S N
Physics 102: Lecture 9, Slide 12
Current loops act like dipoles
Orbits of electrons
“spin”
Electron orbit and “spin” are current loops
Why some materials are magneticNuclear Magnetic Resonance (NMR) and MRI
Physics 102: Lecture 9, Slide 13
B
Compare the torque on loop 1 and 2 which have identical area, and current.
I
ACT: Torque
(1)
B
I
(2)
1) 1 > 2 2) 1 = 2 3) 1 < 2
Area points out of page for both!
= 90 = I A B sin()
Physics 102: Lecture 9, Slide 14
Currents create magnetic fields• Straight wire carrying current I generates a field B
at a distance r:
Mag
nitu
de
Direct
ion
• “Right-hand rule 2”:– Thumb of right hand along I– Fingers of right hand along r– Out-of-palm points along B
𝐵= 𝜇0𝐼2𝜋𝑟 𝜇0 = 4𝜋× 10−7𝑇𝑚/𝐴 “Permeability of free space”(similar to 0 for electricity)
Note: there are different versions of RHR
I (out of page)
B
r
B field circles wire
Physics 102: Lecture 9, Slide 15
A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v
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)
v
I
v(a)
r• •
r(b)
FF
ACT/Preflight 9.6
q q
Physics 102: Lecture 9, Slide 16
Two long wires carry opposite current
What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”?
x
ACT: Adding Magnetic Fields
1) Left 2) Right 3) Up 4) Down 5) Zero
Physics 102: Lecture 9, Slide 17
Force between current-carrying wires
B
Another I towards us
F
Currents in same direction attract!
I towards us
B
Another I away from us
F
Currents in opposite direction repel!
Currents in same direction Currents opposite direction
I towards us
Physics 102: Lecture 9, Slide 18
Comparison:Electric Field vs. Magnetic Field
Electric MagneticSource Charges Moving ChargesActs on Charges Moving ChargesForce F = Eq F = q v B sin()Direction Parallel E Perpendicular to v,B
Field Lines+
Opposites Charges Attract Currents Repel
Physics 102: Lecture 9, Slide 19
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
ACT: Force between Wires
Physics 102: Lecture 9, Slide 20
𝐵= 𝜇0𝑛𝐼
BIB
I
𝜇0 = 4𝜋× 10−7𝑇𝑚/𝐴
B is uniform everywhere inside of solenoid:
n is the number of turns of wire/meter (n = N/L)
B field lines look like bar magnet! Solenoid has N and S poles!
Solenoids
Mag
nitu
de
Direct
ion • Use “Right-hand rule 2”
• A solenoid consists of N loops of wire
Physics 102: Lecture 9, Slide 21
(1) Attractive
(2) Zero
(3) Repulsive
ACT: The force between the two solenoids is …
Physics 102: Lecture 9, Slide 22
Summary of Right-Hand Rules
B
I
B
I
r
RHR 1 RHR 2 Alternate
Force on moving q
B field from current I
Straight wire
Solenoid
I