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Magnet Forces and Magnetic Fields
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1) Magnets and Magnetic Fields
a) Natural permanent magnets– Like poles repel, unlike attract– come in pairs (no monopoles)– Interact with earth;
define N (or north-seeking) pole as pole attracted to North pole of earth
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b) Magnetic field direction:
- direction of force on N pole
B
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c) Field of dipole
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d) Magnetostatics for poles
(identical to electrostatics for charges)– 2 types: N, S vs +,-– Unlike attract, like repel– Inverse square law– Force along joining line– Magnetic Field:
B
F
qM
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e) Why study magnetism?– No monopoles (yet)– Poles (dipoles) produced by moving charges (no direct
control of pole distribution)– Charges affected by magnetic field
i.e. fundamental unit is still charge; want magnetic field due to charge, and force on charge due to magnetic field
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2) Magnetic field due to current (direction)
• Oersted (1820)
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B I
r
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3) Magnetic force on current
Direction from RHR1: B fingers, I thumb, F palm
F
IB
Force per unit length
defines B
a) Orthogonal case
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Bearth .5 gauss 5 10 5 T
Bfridge magnet .01T
Bsuper conducing 1 10 T
B F
I
N
Amtesla (T)Units:
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b) General case
F
LIBsin
Force per unit length
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4) Force between parallel wires
B I1
d;
F
I2B
F
k
I1I2
d
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Attraction or repulsion?
Does it depend on reference frame?
+
+
FE
FE
FB
FB
v
v
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v
v
+
+
-
-
+
+
-
-
+
+
-
-
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• Define Ampere as the quantity of current that produces a force per unit length of 2 x 10-7 N/m for separation of 1 m
F
k
I1I2
d
k 1
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8.988 109Nm2/C2
k (2 10 7 N/m)(1m)
(1A2)2 10 7N/A2• Then
• This defines C and gives
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• Permeability of free space
0 2 k
F
0
2I1I2
dThen
4 10 7N/A2
k 0
2
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5) Field due to long straight wire (magnitude)
B I
r
B 0
2I
r
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6) Force on a moving charge
• Zero at rest
• Zero parallel to B
• Max perpendicular to B
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F qvBsin(Alternative definition of B)
• Proportional to component of v perp to B
• Perpendicular to B
• Perpendicular to v
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7) Motion of a charge in a magnetic field
a) Constant force
motion is parabolic
electric or gravitational field
not everywhere perp to velocity
not magnetic field
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b) Constant magnitude perpendicular to motion
radial field (circular motion)
mass on a string
magnetic field produces circular motion
(initial vel. perp. to B)
motion is circular
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F Fc mv 2
r
Force due to the field:
F qvB
For circular motion:
So,
mv 2
rqvB
r mv
qBr depends on v, B
v
r
qB
m
angular freq. independent of speed, radius
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Tracks in a bubble chamber
• electron-positron creation
• 1, 3 positive
• 2 negative
• energy: 3 > 2 > 1
• energy decreases by collisions
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Example: Find speed and radius for proton
B = 0.10 T
V = 2100 V
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c) Work done by magnetic field
W Fx cosF
displacement, x
Work by a force F
For a magnetic field,
0
Work = 0
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d) Velocity selector
FE qE
Force due to E (down):
Force due to B (up):
FB qvB
For zero deflection, FE = FB :
qE qvB
v E
B
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e) Mass SpectrometerIon energy:
KE 12 mv 2 qV
v 2qV
m
Radius of motion:
r mv
qB
m
qB
2qV
m
r m
q
2V
B
m
q
r2B2
2V