Transcript PowerPoint Presentation - Chapter 21 Magnetic forces and

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Chapter 21
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:
F
B
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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I
B
r
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3) Magnetic force on current
a) Orthogonal case
Force per unit length
F
 IB
defines B
Direction from RHR1: B fingers, I thumb, F palm
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Units:

F
N
B 
 tesla (T )
I
Am
Bearth  .5 gauss  5 105 T
Bfridge magnet  .01T
Bsuper conducing  110 T
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b) General case
Force per unit length
F
 IBsin
L
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4) Force between parallel wires
I1
B ;
d
F

F
 I2 B
I1I2
 k 
d
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FE
+
FB
FB
+
v
v
FE
Attraction or repulsion?
Does it depend on reference frame?
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-
-
+
+
-
-
+
+
-
-
+
v
+
v
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F
I1I2
 k 
d
• 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

• Then
(2 107 N/m)(1m)
7
2

k 
 2 10 N/A
2
(1A )
• This defines C and gives

k
1
40
 8.98810 Nm /C
9
2
2
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• Permeability of free space
0  2k   4  10 N/A
7

Then
F
0 I1I2

2 d
2
0
 k  
2
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5) Field due to long straight wire (magnitude)
I
B
r

0 I
B
2 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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• Proportional to component of v perp to B
F  qvB sin
(Alternative definition of 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
motion is circular
magnetic field produces
circular motion
(initial vel. perp. to B)
Force due to the field:
F  qvB
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For circular motion:
2
mv

F  Fc 
r
So,

r

mv

qB
mv 2
 qvB
r
r depends on v, B
v
qB
 
r
m
angular freq.
independent of
speed, radius
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
Work by a force F
F


displacement, x
W  Fx cos 
For a magnetic field,   0
Work = 0

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d) Velocity selector
Force due to E (down):
FE  qE
Force due to B (up):

FB  qvB
For zero deflection, FE = FB :


qE  qvB
E
v
B
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e) Mass Spectrometer
Ion energy:
KE  m v  qV  v 
1
2

Radius of motion:
mv  m 2qV
r

qB
qB m
r


2
m
q
2V
B

m r 2B 2

q
2V
2qV
m