recap i lecture 15 - cornell universityliepe/webpage/docs/phys... · 2012-02-24 · recap ii ....
TRANSCRIPT
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Recap I Lecture 15
© Matthias Liepe, 2012
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Recap II
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Today:
• Particle accelerators: The cyclotron and synchrotron
• Crossed electric and magnetic fields
• Velocity selector
• Hall effect
• Magnetic force on a current carrying wire
• Torque on a current loop
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A particle of mass m and charge q 0 is moving with speed v to a uniform magnetic field B.
m
q 0
B
uniform
v
How is the period T of the particle’s orbit related to its speed v?
A. T v B. T v 2 C. T v 1 D. T v12 E. T does not depend on v
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Application: Particle Accelerators
B
uniform
~ oscillating voltage source
of frequency fosc
dee
The cyclotron:
• Fixed magnetic field; changing orbit radius
• composed of two hollow copper dees that are immersed in a uniform magnetic field & connected to an oscillating voltage source.
• Particles (e.g., protons), each of charge q & mass m, start at a source near the center of the dees.
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The Cornell Cyclotron
The Cornell cyclotron (2 MeV protons) was built about 1935 and decommissioned in 1956. This photo with Assistant Professor Boyce D. McDaniel was taken in 1955.
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Application: Particle Accelerators
The synchrotron:
• Fixed orbit radius; magnetic field adjusted for particle momentum/energy
• “Dipole magnets” keep particles on fixed orbit.
const.)(
)(
tqB
tpRadius
v
B
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The Cornell Synchrotron
• Radius = 122 m • Particle energy: up to 5 GeV • Magnetic bending fields: up to
~0.2 T (~3000* Earth’s magnetic field)
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Crossed Electric and Magnetic Fields
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m
B
uniform
v
A particle of mass m and charge q 0 is moving with speed v to a uniform magnetic field B. By applying a uniform electric field E in the same region as the magnetic field, the particle can be made to move in a straight line with constant speed v.
What should be the direction of the electric field?
A. B. C. D. (out of) E. (into)
Velocity Selector:
q 0
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What should be the magnitude of the electric field?
A. qvB B. q2vB C. vB D. mv(qB) E. B
m
B
uniform
v
A particle of mass m and charge q 0 is moving with speed v to a uniform magnetic field B. By applying a uniform electric field E in the same region as the magnetic field, the particle can be made to move in a straight line with constant speed v.
Velocity Selector:
q 0
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Mass Spectrometer
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i
e dv
e dv
B
uniform on turn
steady state
dv
e HE
Hall Effect
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dv
e HE
B
uniform
V measures ‘Hall voltage’ VH EHd
d
What is the drift speed vd of the mobile electrons?
A. VH(deB) B. VH(de2B) C. VH(dB) D. None of the above
i
VH
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i
Hall Effect:
dv
e HE
B
uniform
V VH EHd
d VH
Production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current.
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i
If current is sent through the Aluminum bar that’s between the magnet poles in the direction shown, which way will the bar move?
A. B. C. That bar won’t move!