ubc physics 102
TRANSCRIPT
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UBC Physics 102Lecture 11
Rik Blok
http://www.zoology.ubc.ca/˜rikblok/phys102/lecture/ UBC Physics 102: Lecture 11, July 16, 2003 – p. 1/20
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Outline
B Magnetic fieldB Electric currentsB Force on currentB Force on a chargeB Torque on a current loopB End
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Magnetic field [Text: Sect. 27-1]
Definition: dipole
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Magnetic field [Text: Sect. 27-1]
Definition: dipoleObject with two opposite ends.
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Magnetic field [Text: Sect. 27-1]
Definition: dipoleObject with two opposite ends.Magnetic “charges” always come as dipoles.
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Magnetic field [Text: Sect. 27-1]
Definition: dipoleObject with two opposite ends.Magnetic “charges” always come as dipoles.Ends are called North (+) and South (−).
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Magnetic field [Text: Sect. 27-1]
Definition: dipoleObject with two opposite ends.Magnetic “charges” always come as dipoles.Ends are called North (+) and South (−).Unlike electricity, magnetic dipoles cannot beseparated into poles.
Electricity Magnetism
−
−
+
+
SS
S
NN
N
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Magnetic field [Text: Sect. 27-1]
Definition: dipoleObject with two opposite ends.Magnetic “charges” always come as dipoles.Ends are called North (+) and South (−).Unlike electricity, magnetic dipoles cannot beseparated into poles.
Electricity Magnetism
−
−
+
+
SS
S
NN
N
Is the main (only?) difference between electricity andmagnetism.
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Magnetic field, contd
Discussion: Magnetic field, B
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Magnetic field, contd
Discussion: Magnetic field, B
Analogous to electric field. Denoted by B.
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Magnetic field, contd
Discussion: Magnetic field, B
Analogous to electric field. Denoted by B.Comes out of N end of magnet, goes into S.
S N
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Magnetic field, contd
Discussion: Magnetic field, B
Analogous to electric field. Denoted by B.Comes out of N end of magnet, goes into S.
S N
Magnetic field creates force on nearby magnets.
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Magnetic field, contd
Discussion: Magnetic field, B
Analogous to electric field. Denoted by B.Comes out of N end of magnet, goes into S.
S N
Magnetic field creates force on nearby magnets.Like poles repel, opposites attract.
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Magnetic field, contd
Discussion: Magnetic field, B
Analogous to electric field. Denoted by B.Comes out of N end of magnet, goes into S.
S N
Magnetic field creates force on nearby magnets.Like poles repel, opposites attract.N end of compass (magnet) points along direction ofmagnetic field (N to S).
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Magnetic field, contd
Discussion: Magnetic field, B
Analogous to electric field. Denoted by B.Comes out of N end of magnet, goes into S.
S N
Magnetic field creates force on nearby magnets.Like poles repel, opposites attract.N end of compass (magnet) points along direction ofmagnetic field (N to S).
Interactive Quiz: PRS 11a
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Magnetic field, contd
Discussion: The earth as a magnet
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Magnetic field, contd
Discussion: The earth as a magnetCompasses point north so earth has magnetic field.
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Magnetic field, contd
Discussion: The earth as a magnetCompasses point north so earth has magnetic field.But compasses point from N to S!
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Magnetic field, contd
Discussion: The earth as a magnetCompasses point north so earth has magnetic field.But compasses point from N to S!Because earth’s “north” pole is really magnetic S.
S
N
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Magnetic field, contd
Discussion: The earth as a magnetCompasses point north so earth has magnetic field.But compasses point from N to S!Because earth’s “north” pole is really magnetic S.
S
N
Maybe due to currents of ionized molten metal(http://istp.gsfc.nasa.gov/earthmag/dynamos2.htm ).
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Electric currents [Text: Sect. 27-2]
Discussion: Electric currents
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Electric currents [Text: Sect. 27-2]
Discussion: Electric currentsMoving charges produce magnetic field.
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Electric currents [Text: Sect. 27-2]
Discussion: Electric currentsMoving charges produce magnetic field.Current (moving charges in wire) does too.
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Electric currents [Text: Sect. 27-2]
Discussion: Electric currentsMoving charges produce magnetic field.Current (moving charges in wire) does too.Direction of B-field found to be ⊥ to current.
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Electric currents [Text: Sect. 27-2]
Discussion: Electric currentsMoving charges produce magnetic field.Current (moving charges in wire) does too.Direction of B-field found to be ⊥ to current.In straight wire field has to circle around wire.
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Electric currents [Text: Sect. 27-2]
Discussion: Electric currentsMoving charges produce magnetic field.Current (moving charges in wire) does too.Direction of B-field found to be ⊥ to current.In straight wire field has to circle around wire.But which way?
I
B
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Electric currents, contd
Definition: Right-hand field rule
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Electric currents, contd
Definition: Right-hand field rule
“Grasp” wire in right hand.
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Electric currents, contd
Definition: Right-hand field rule
“Grasp” wire in right hand.
Point thumb in direction of current.
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Electric currents, contd
Definition: Right-hand field rule
“Grasp” wire in right hand.
Point thumb in direction of current.Then fingers wrap around in direction of field.
I
B
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Electric currents, contd
Definition: Right-hand field rule
“Grasp” wire in right hand.
Point thumb in direction of current.Then fingers wrap around in direction of field.
I
B
Interactive Quiz: PRS 11b
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Force on current [Text: Sect. 27-3]
Discussion: Force on current
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Force on current [Text: Sect. 27-3]
Discussion: Force on currentCurrent exerts force on magnet (eg. turns compassto line up with B-field).
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Force on current [Text: Sect. 27-3]
Discussion: Force on currentCurrent exerts force on magnet (eg. turns compassto line up with B-field).Opposite holds too: magnet exerts force oncurrent-carrying wire.
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Force on current [Text: Sect. 27-3]
Discussion: Force on currentCurrent exerts force on magnet (eg. turns compassto line up with B-field).Opposite holds too: magnet exerts force oncurrent-carrying wire.Force ⊥ to both current and B-field.
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Force on current [Text: Sect. 27-3]
Discussion: Force on currentCurrent exerts force on magnet (eg. turns compassto line up with B-field).Opposite holds too: magnet exerts force oncurrent-carrying wire.Force ⊥ to both current and B-field.But that still leaves 2 possible directions. . .
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Force on current, contd
Definition: Right-hand force rule
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Force on current, contd
Definition: Right-hand force rule
Point index finger of right hand in direction ofcurrent, I.
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Force on current, contd
Definition: Right-hand force rule
Point index finger of right hand in direction ofcurrent, I.Bend middle finger to direction of B-field.
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Force on current, contd
Definition: Right-hand force rule
Point index finger of right hand in direction ofcurrent, I.Bend middle finger to direction of B-field.Then thumb points in direction of force, F.
I
B
F
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Force on current, contd
Discussion: 3d convention
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Force on current, contd
Discussion: 3d conventionDealing with 3 ⊥ directions, 3-dimensions.
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Force on current, contd
Discussion: 3d conventionDealing with 3 ⊥ directions, 3-dimensions.Convention for drawing 3d arrows on paper.
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Force on current, contd
Discussion: 3d conventionDealing with 3 ⊥ directions, 3-dimensions.Convention for drawing 3d arrows on paper.⊙
= arrow coming out of page (looking at ithead-on).
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Force on current, contd
Discussion: 3d conventionDealing with 3 ⊥ directions, 3-dimensions.Convention for drawing 3d arrows on paper.⊙
= arrow coming out of page (looking at ithead-on).⊗
= arrow going into page (looking at the tail).
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Force on current, contd
Discussion: 3d conventionDealing with 3 ⊥ directions, 3-dimensions.Convention for drawing 3d arrows on paper.⊙
= arrow coming out of page (looking at ithead-on).⊗
= arrow going into page (looking at the tail).
Interactive Quiz: PRS 11c
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Force on current, contd
Definition: Magnetic field, B
I
B⊥B
θ
l
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Force on current, contd
Definition: Magnetic field, B
I
B⊥B
θ
l
B-field defined by force it exerts on current,
F = IlB⊥.
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Force on current, contd
Definition: Magnetic field, B
I
B⊥B
θ
l
B-field defined by force it exerts on current,
F = IlB⊥.
B⊥ = B sin θ is component of B perpendicular to I.http://www.zoology.ubc.ca/˜rikblok/phys102/lecture/ UBC Physics 102: Lecture 11, July 16, 2003 – p. 11/20
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Force on current, contd
Unit: Tesla, T, and Gauss, G
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Force on current, contd
Unit: Tesla, T, and Gauss, G
Units of magnetic field strength.
1 T = 1 N/A · m,
1 G = 10−4
T.
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Force on a charge[Text: Sect. 27-4]
Discussion: Force on a charge
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Force on a charge[Text: Sect. 27-4]
Discussion: Force on a chargeCurrent-carrying wire contains charges q moving atspeed v.
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Force on a charge[Text: Sect. 27-4]
Discussion: Force on a chargeCurrent-carrying wire contains charges q moving atspeed v.Can work out that force on each charge must be
F = qvB⊥.
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Force on a charge[Text: Sect. 27-4]
Discussion: Force on a chargeCurrent-carrying wire contains charges q moving atspeed v.Can work out that force on each charge must be
F = qvB⊥.
Direction again given by right-hand force rule, bysubstituting I → qv.
qv
B
F
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Force on a charge, contd
Discussion: Force on a charge, contd
http://www.zoology.ubc.ca/˜rikblok/phys102/lecture/ UBC Physics 102: Lecture 11, July 16, 2003 – p. 14/20
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Force on a charge, contd
Discussion: Force on a charge, contdNote: index finger along qv so if q < 0 then fingerpoints against direction of velocity, v.
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Force on a charge, contd
Discussion: Force on a charge, contdNote: index finger along qv so if q < 0 then fingerpoints against direction of velocity, v.
Interactive Quiz: PRS 11d
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Force on a charge, contd
Discussion: Force on a charge, contdNote: index finger along qv so if q < 0 then fingerpoints against direction of velocity, v.
Interactive Quiz: PRS 11dExample: Path in a uniform magnetic field
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Force on a charge, contd
Discussion: Force on a charge, contdNote: index finger along qv so if q < 0 then fingerpoints against direction of velocity, v.
Interactive Quiz: PRS 11dExample: Path in a uniform magnetic field
Describe the path of a charged particle, q, moving atspeed v in a magnetic field perpendicular to amagnetic field B.
http://www.zoology.ubc.ca/˜rikblok/phys102/lecture/ UBC Physics 102: Lecture 11, July 16, 2003 – p. 14/20
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Force on a charge, contd
Discussion: Force on a charge, contdNote: index finger along qv so if q < 0 then fingerpoints against direction of velocity, v.
Interactive Quiz: PRS 11dExample: Path in a uniform magnetic field
Describe the path of a charged particle, q, moving atspeed v in a magnetic field perpendicular to amagnetic field B.
Solution: Path in a uniform magnetic field
http://www.zoology.ubc.ca/˜rikblok/phys102/lecture/ UBC Physics 102: Lecture 11, July 16, 2003 – p. 14/20
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Force on a charge, contd
Discussion: Force on a charge, contdNote: index finger along qv so if q < 0 then fingerpoints against direction of velocity, v.
Interactive Quiz: PRS 11dExample: Path in a uniform magnetic field
Describe the path of a charged particle, q, moving atspeed v in a magnetic field perpendicular to amagnetic field B.
Solution: Path in a uniform magnetic fieldIf the particle’s velocity is ⊥ to B then the force isF = qvB and ⊥ to both v and B.
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Force on a charge, contd
Solution: Path in a uniform magnetic field,contd
This will cause the particle to accelerate sidewaysfrom its original path.
v
B⊙
Fq
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Force on a charge, contd
Solution: Path in a uniform magnetic field,contd
This will cause the particle to accelerate sidewaysfrom its original path.But B is still ⊥ to v so will accelerate sidewaysrelative to new path.
v
B⊙
Fq
v
B⊙
F
q
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Force on a charge, contd
Solution: Path in a uniform magnetic field,contd
This will cause the particle to accelerate sidewaysfrom its original path.But B is still ⊥ to v so will accelerate sidewaysrelative to new path.
v
B⊙
Fq
v
B⊙
F
q
Particle feels constant force, always pulling to theside.http://www.zoology.ubc.ca/˜rikblok/phys102/lecture/ UBC Physics 102: Lecture 11, July 16, 2003 – p. 15/20
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Force on a charge, contd
Solution: Path in a uniform magnetic field,contd
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Force on a charge, contd
Solution: Path in a uniform magnetic field,contd
Motion is a circle. Recall, acceleration towards thecenter of a circle is a = v
2
r.
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Force on a charge, contd
Solution: Path in a uniform magnetic field,contd
Motion is a circle. Recall, acceleration towards thecenter of a circle is a = v
2
r.
From F = ma can find radius of circle,
F = ma
qvB = mv2
r
r =mv
qB.
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Force on a charge, contd
Solution: Path in a uniform magnetic field,contd
Motion is a circle. Recall, acceleration towards thecenter of a circle is a = v
2
r.
From F = ma can find radius of circle,
F = ma
qvB = mv2
r
r =mv
qB.
So motion is a circle with radius r.
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Torque on a current loop [Text: Sect. 27-5]
Discussion: Current loop in B-field
I
B
w
l
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Torque on a current loop [Text: Sect. 27-5]
Discussion: Current loop in B-field
I
B
w
l
Force F = IlB into page on left side and out of pageon right.
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Torque on a current loop [Text: Sect. 27-5]
Discussion: Current loop in B-field
I
B
w
l
Force F = IlB into page on left side and out of pageon right.Causes loop to turn around center axis (torque or“angular force,” see Ch. 10).
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Torque on a current loop, contd
Discussion: Electric motors
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Torque on a current loop, contd
Discussion: Electric motorsLooking at loop from top-down:
BBB
F
F
F
F
F
FI
⊙I⊙
I⊙
I⊗
I⊗I
⊗
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Torque on a current loop, contd
Discussion: Electric motorsLooking at loop from top-down:
BBB
F
F
F
F
F
FI
⊙I⊙
I⊙
I⊗
I⊗I
⊗
So loop won’t keep rotating.
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Torque on a current loop, contd
Discussion: Electric motorsLooking at loop from top-down:
BBB
F
F
F
F
F
FI
⊙I⊙
I⊙
I⊗
I⊗I
⊗
So loop won’t keep rotating.But if we reverse direction of current when at middle:
BBB
FF
F
F
I⊙I
⊙I
⊗
I⊗
I = 0
I = 0
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Torque on a current loop, contd
Discussion: Electric motors, contd
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Torque on a current loop, contd
Discussion: Electric motors, contdCauses loop to spin, which can do work.
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Torque on a current loop, contd
Discussion: Electric motors, contdCauses loop to spin, which can do work.Basic principle of electric motors.
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End
Practice Problems:Ch. 27: Q. 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25.Ch. 27: Pr. 1, 3, 5, 7, 9, 13, 15, 21, 23, 25, 31, 35,51, 55, 57, 61, 63, 65, 67.
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End
Practice Problems:Ch. 27: Q. 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25.Ch. 27: Pr. 1, 3, 5, 7, 9, 13, 15, 21, 23, 25, 31, 35,51, 55, 57, 61, 63, 65, 67.
Interactive Quiz: Feedback
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End
Practice Problems:Ch. 27: Q. 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25.Ch. 27: Pr. 1, 3, 5, 7, 9, 13, 15, 21, 23, 25, 31, 35,51, 55, 57, 61, 63, 65, 67.
Interactive Quiz: FeedbackTutorial Question: tut11
http://www.zoology.ubc.ca/˜rikblok/phys102/lecture/ UBC Physics 102: Lecture 11, July 16, 2003 – p. 20/20