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Phys 272 1

1)   Moving charges (currents) create a magnetic field B.
(Units: Tesla)
2)   B will exert a magnetic force on any other moving charge or current.
F=qvBsin θ !
Direction given by right-hand rule.
3) Because F perp v, magnetic force does zero work.
4) Force doesn’t change kinetic energy of moving charge.
Instead the force deflects the path of the charge.
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Velocity Selector q v
X
B
Make a beam of charged particles enter a region of crossed E and B fields.
E
E is down and B is into paper so that E perpendicular to B.
F
E
is down and F
B
is up.
If beam is not deflected, F
E
So qE=qvB !
v=E/B
=F
B
.
Only particles with this speed will get through the slit.
Phys 272 3

28.8: Magnetic Force on a
Current-Carrying Wire:
Force on a current carrying wire in a uniform magnetic field
B points out of the screen
Force on the charges is transmitted to the wire
F =
qv B = L A n qv B = i L B

28.8: Magnetic Force on a
Current-Carrying Wire:
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i-clicker:
Current is going up in the wire which is in a magnetic field pointing to the right. In which direction is the force on the wire?
I a)   Out of the paper.
B b)   Into the paper.
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i-clicker:
Current is going up in the wire which is in a magnetic field pointing to the right. In which direction is the force on the wire?
I a)   Out of the paper. b)   Into the paper.
B
Answer is B!
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28.9: Torque on a Current Loop:
The two magnetic forces F and – F produce a torque on the loop, tending to rotate it about its central axis.
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28.9: Torque on a Current Loop:
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Phys 272 10

29.2: Calculating the Magnetic Field due to a Current: Biot-Savart Law
Wire carries current I. Length element ds creates field element dB at point P.
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29.2: Magnetic Field due to a Long Straight Wire:
Fig. 29-4 A right-hand rule gives the direction of the magnetic field due to a current in a wire. ( a) The magnetic field B at any point to the left of the wire is perpendicular to the dashed radial line and directed into the page, in the direction of the fingertips, as indicated by the x. ( b) If the current is reversed, at any point to the left is still perpendicular to the dashed radial line but now is directed out of the page, as
Phys 272 12

29.2: Magnetic Field due to a Long Straight Wire:
At Point P, dB points into screen, because of ds × r
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29.2: Magnetic Field due to a Long Straight Wire:
The magnitude of the magnetic field at a perpendicular distance R from a long (infinite) straight wire carrying a current i is given by
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Fig. 29-3 Iron filings that have been sprinkled onto cardboard collect in concentric circles when current is sent through the central wire. The alignment, which is along magnetic field lines, is caused by the magnetic field produced by the current. (Courtesy Education
Development Center)

29.2: Magnetic Field due to a Current in a Circular Arc of Wire:
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Ex: B at center of circular loop
I ( ds )(1) sin 90 dB =
µ o
4 R 2
True for every ds around circle. Integrate:
B =
µ o
I (2 R
=
µ o
I
4 R 2 2 R
Use right-hand rule for direction! B "
I ds
R
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Ex:
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Ex:
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Ex: Two wires carry currents “I” and “3I” as shown.
Where is B=0?
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Ex: Two wires carry currents “I” and “3I” as shown.
Where is B=0?
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Ex: Two wires carry currents “I” and “3I” as shown.
Where is B=0?
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Ex: Equal and opposite currents as shown. Find B on x-axis.
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Ex: Equal and opposite currents as shown. Find B on x-axis.
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i-clicker:
Where on the x-axis (excluding infinity) is B tot
=0? a)   At a point x <0 b)   At a point x such that 0 < x <d c)   At a point x >d d)   Only at infinity
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i-clicker:
Where on the x-axis (excluding infinity) is B tot
=0? a)   At a point x <0 b)   At a point x such that 0 < x <d c)   At a point x >d d)   Only at infinity
Answer: b
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29.3: Force Between Two Parallel Wires:
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i-clicker:
What is the direction of the net force on the rectangular loop? a)   To the right b)   To the left c)   Towards wire 1 d)   Away from wire 1
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i-clicker:
What is the direction of the net force on the rectangular loop? a)   To the right b)   To the left c)   Towards wire 1 d)   Away from wire 1
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F
AB
>F
CD
(closer) Answer is c
Phys 272 28