Transcript Physics 2102 Spring 2002 Lecture 8

Physics 2102
Aurora Borealis
Jonathan Dowling
Lecture 19: MON 02 MAR
Magnetic fields
Ch.28.6-7
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“I’ll be back….
Second Exam Review:
6-7PM WED 04 MAR
Nicholson 130
Second Exam (Chapters 24–28):
6–7PM THU 05 MAR
Lockett 6
Circular Motion:
v
F
Since magnetic force is perpendicular to motion,
the movement of charges is circular.
2
v
out
2
Fcentrifugal  ma  mr   m
r
in
magnetic
r
F
 qvB
FB  FC
m v2
 qv B 
r

B into blackboard.



mv
Solve : r 
qB
In general, path is
a helix (component of v parallel to
field is unchanged).
v
F
C
.
.B
electron
mv
r
qB
Radius of Circlcular Orbit
r

v qB
 
r m
2r 2mv 2m
T


v
qBv
qB
Angular Frequency:
Independent of v
Period of Orbit:
Independent of v

1 qB
f  
T 2m
Orbital Frequency:
Independent of v
Example
Two charged ions A and B traveling with a
constant velocity v enter a box in which
there is a uniform magnetic field directed
out of the page. The subsequent paths
are as shown. What can you conclude?
A
v
B
v
(a) Both ions are negatively charged.
(b) Ion A has a larger mass than B.
(c) Ion A has a larger charge than B.
mv
r
qB
(d) None of the above.
Same charge q, speed v, and same B for both masses.
So: ion with larger mass/charge ratio (m/q) moves in circle of larger
radius. But that’s all we know! Don’t know m or q separately.
Examples of Circular Motion in
Magnetic Fields
Aurora borealis
(northern lights)
Synchrotron
Suppose you wish to accelerate charged
particles as fast as you can.
Linear accelerator (long).
Fermilab,
Batavia, IL (1km)
Magnetic Force on a Wire.
L
L
q  it  i
vd

 
F  q vd  B


iL   
F  q B iLB
q

 
F iLB
Note: If wire is not straight,
compute force on differential
elements and integrate:

 
dF  i dL  B
Example
Wire with current i.
Magnetic field out of page.
What is net force on wire?
F1  F3  iLB
dF  iBdL  iBRd
By symmetry, F2 will only
have a vertical component,


0
0
F2   sin( )dF iBR  sin( )d 2iBR
Ftotal  F1  F2  F3  iLB  2iRB  iLB  2iB( L  R)
Notice that the force is the same as that for a straight wire,
and this would be true no
matter what the shape of
L
R
R
L
the central segment!.
Example 4: The Rail Gun
• Conducting projectile of length
2cm, mass 10g carries constant
current 100A between two rails.
• Magnetic field B = 100T points
outward.
• Assuming the projectile starts
from rest at t = 0, what is its
speed after a time t = 1s?
• Force on projectile: F= iLB
• Acceleration: a = F/m = iLB/m
• v = at = iLBt/m
rails
B
I
L
projectile
(from F = iL x B)
(from F = ma)
(from v = v0 + at)
= (100A)(0.02m)(100T)(1s)/(0.01kg) = 2000m/s
= 4,473mph = MACH 8!
Rail guns in the “Eraser” movie
"Rail guns are hyper-velocity weapons that shoot aluminum or clay rounds at just
below the speed of light. In our film, we've taken existing stealth technology one
step further and given them an X-ray scope sighting system," notes director
Russell. "These guns represent a whole new technology in weaponry that is still
in its infancy, though a large-scale version exists in limited numbers on
battleships and tanks. They have
incredible range. They can pierce
three-foot thick cement walls and
then knock a canary off a tin can with
absolute accuracy. In our film, one
contractor has finally developed an
assault-sized rail gun. We researched
this quite a bit, and the technology is
really just around the corner, which is
one of the exciting parts of the story."
Warner Bros., production notes, 1996.
http://movies.warnerbros.com/eraser/cmp/prodnotes.html#tech
Also: INSULTINGLY STUPID MOVIE PHYSICS: http://www.intuitor.com/moviephysics/
Electromagnetic Slingshot
These Devices Can
Launch 1000kg Projectiles
At Mach 100 at a Rate of
1000 Projectiles Per Second.
Using KE = 1/2mv2
This corresponds to an output
about 1012 Watts = TeraWatt.
Uses: Put Supplies on Mars.
Destroy NYC in about 10
minutes.
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