1 w06d2 magnetic forces and sources of magnetic fields w06d2 magnetic force on current carrying...
TRANSCRIPT
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W06D2 Magnetic Forces and Sources of
Magnetic Fields
W06D2 Magnetic Force on Current Carrying Wire, Sources of Magnetic Fields: Biot-Savart Law
Reading Course Notes: Sections 8.3, 9.1-9.2
Announcements
Review Week 6 Tuesday from 9-11 pm in 26-152
PS 6 due Week 6 Tuesday at 9 pm in boxes outside 32-082 or 26-152
W06D3 PS05: Calculating Magnetic Fields and Magnetic Force Reading Course Notes: Sections 8.9, 8.10, 9.10.1, 9.11.1-.3, 9.11.7-.8
Exam 2 Thursday March 21 7:30 - 9:30 pm
Conflict Exam 2 March 22 9-11 am or 10-12 noon
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Outline
Magnetic Force on Current Carrying Wire
Sources of Magnetic Fields
Biot-Savart Law
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Magnetic Force on Current-Carrying Wire
Current is moving charges, and we know that moving charges feel a force in a magnetic field
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magd dq F v B
Magnetic Force on Current-Carrying Wire
d dqdq dq d Id
dt dt
sv s s
magd Id F s B
mag
wire
Id F s B
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Magnetic Force on Current-Carrying Wire
mag
wire
Id
F s B
If the wire is a uniform magnetic field then
If the wire is also straight then
mag ( )I F L B
Demonstration:Wire in a Magnetic Field (Jumping
Wire) G8
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magd Id F s B
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%208&show=0
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Demonstration:
Series or Parallel Current Carrying Wires G9
You tube video of experiment showing parallel wires attracting
http://youtu.be/rU7QOukFjTo
or repelling:
http://youtu.be/bnbKdbXofEI
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%209&show=0
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Group Problem: Current Loop
A conducting rod of uniform mass per length is suspended by two flexible wires in a uniform magnetic field of magnitude B which points out of the page and a uniform gravitational field of magnitude g pointing down. If the tension in the wires is zero, what is the magnitude and direction of the current in the rod?
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Sources of Magnetic Fields
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What Creates Magnetic Fields: Moving Charges
http://youtu.be/JmqX1GrMYnU
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Electric Field Of Point Charge
An electric charge produces an electric field:
2
1ˆ
4 o
q
rE r
r̂ : unit vector directed from the charged object
to the field point P
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Magnetic Field Of Moving Charge
Moving charge with velocity v produces magnetic field:
2
ˆx
4o q
r
v r
B
:r̂ unit vector directed from charged object to P
r̂
permeability of free space 04 10 7 T m A 1
P
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Currents are Sources of Magnetic Field
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Demonstration:Field Generated by Wire G12
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%2012&show=0
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Continuous Moving Charge Distributions:
Currents & Biot-Savart
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d dqB v From Charges to Currents?
[coulomb]
[meter]
[sec]
d dqd dq dq d Id
dt dt
sB v s s
[coulomb]
[sec][meter]
v
dq
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The Biot-Savart Law
Current element of length ds pointing in direction of current I produces a magnetic field:
02
ˆ
4
I dd
r
s rB
http://web.mit.edu/viz/EM/visualizations/magnetostatics/MagneticFieldConfigurations/CurrentElement3d/CurrentElement.htm
ds
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The Right-Hand Rule #2
ˆ ˆˆdir ( )P B z r
ˆdir d s z
P18-20
Concept Question: Biot-Savart
The magnetic field at P points towards the
1. +x direction2. +y direction3. +z direction4. -x direction5. -y direction6. -z direction7. Field is zero
P18-21
Concept Question Answer: Biot-Savart
The vertical line segment contributes nothing to the field at P (it is parallel to the displacement). The horizontal segment makes a field pointing into the page by the right-hand rule # 2 (right thumb in direction of current, fingers curl into page at P.
Answer: 6. is in the negative z direction (into page)
( )PB
dir
P18-22
Concept Question: Bent Wire
The magnetic field at P is equal to the field of:
1. a semicircle2. a semicircle plus the field of a long straight wire3. a semicircle minus the field of a long straight wire4. none of the above
P18-23
Concept Question Answer: Bent Wire
All of the wire makes into the page. The two straight parts, if put together, would make an infinite wire. The semicircle is added to this to get the magnetic field
Answer: 2. Semicircle + infinite wire
dirrB(P)
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Repeat Demonstration:Parallel & Anti-Parallel Currents G9
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%209&show=0
P18-25
Concept Question: Parallel Wires
Consider two parallel current carrying wires. With the currents running in the opposite direction, the wires are
1. attracted (opposites attract?)
2. repelled (opposites repel?)
3. pushed another direction
4. not pushed – no net force
5. I don’t know
P18-26
Concept Q. Answer: Parallel Wires
I1 creates a magnetic field into the
page at wire 2. That makes a force on wire 2 to the right.
I2 creates a magnetic field into the
page at wire 1. That makes a force on wire 1 to the left.
Answer: 1. The wires are repelled
2 2 2 1I F L B
1 1 1 2I F L B
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Can we understand why?Whether they attract or repel can be seen in the shape of the created B field
You tube videos of field line animations showing why showing parallel wires attract: or repel:
http://youtu.be/5nKQjKgS9z0 http://youtu.be/nQX-BM3GCv4
P18-28
Concept Question: Current Carrying Coils
The above coils have1. parallel currents that attract2. parallel currents that repel3. opposite currents that attract4. opposite currents that repel
P18-29
Concept Q. Answer: Current Carrying Coils
Look at the field lines at the edge between the coils. They are jammed in, want to push out. Also, must be in opposite directions
Answer: 4. Opposite currents that repel
http://web.mit.edu/viz/EM/visualizations/magnetostatics/ForceOnCurrents/MagneticForceRepel/MagneticForceRepel.htm
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Example : Coil of Radius R
Consider a coil with radius R and current I
II
IP
Find the magnetic field B at the center (P)
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Example : Coil of Radius R
Consider a coil with radius R and current I
II
IP
1) Think about it:• Legs contribute nothing
I parallel to r• Ring makes field into page
2) Choose a ds
3) Pick your coordinates
4) Write Biot-Savart
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Animation: Magnetic Field Generated by a Current Loop
http://web.mit.edu/viz/EM/visualizations/magnetostatics/calculatingMagneticFields/RingMagInt/RingMagIntegration.htm
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Example: Coil of Radius RIn the circular part of the coil…
ˆd s r
r̂s
d
II
I
02
ˆ
4
dIdB
r
s rBiot-Savart:
ˆ| d | ds s r
0I
4ds
r 2
0I
4R dR2
0I
4dR
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II
I
Example : Coil of Radius RConsider a coil with radius R and current I
s
d
dB
0I
4dR
B dB
0I
4dR
0
2
0I
4 Rd
0
2
0I
4 R2
rB
0I
2Rdirection into page
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Group Problem:B Field from Coil of Radius R
Consider a coil with radius R and carrying a current I
What is B at point P? WARNING:
This is much harder than the previous problem. Why??