Unit 4 Day 4 – Electron Properties & Hall Effect
• Cathode Rays and Cathode Ray Tubes
• Electron Beam in the Presence on an Electric & magnetic Field
• The Velocity Selector
• The Hall Effect & Hall EMF
Cathode Rays• In the 1890’s, devices were built called
discharge tubes
• What was emitted & observed as a “glow” was called cathode rays. It was later determined that these were ionized electrons.
Evacuated butback filled withrarified gas
Cathode Ray Tube
• Cathode Ray Tube (CRT) starts with a beam of electrons which are passed through a set of parallel plates, and a set of coils, 90° to the plates.
• When the E-Field is applied, the electrons curve up. When the B-Field is applied, the electrons curve down.
Br
v
m
eor
r
vmevB
ee
2
Electron Properties• Remember, in previous experiments performed by J. J.
Thompson, if the Electric and Magnetic forces are balanced:
• The electron velocity becomes:
• E, B, & r, were all measurable quantities
B
Ev
or
evBeE
kgC
e rB
E
BrB
E
Br
v
m
e 112 1076.1
Electron Properties
• Note: In later experiments by Millikan (Oil-drop Experiment), the charge of the electron was established.
• Knowing e and e/me, then me was calculated to be:
kgme311011.9
CE
gme
gmeE
drop
drop
1910602.1
The Hall Effect
• If a current carrying conductor is held fixed in a magnetic field, the magnetic force on the electrons in the conductor is:
where vd = drift velocity
• The electron will tend to move to the bottom of the conductor (D)
BveF dB
The Hall Effect
• The movement of the electron will develop a ΔV between the top (C) and the bottom (D) which will set-up an electric field EH.
• This produces an electric force –eEH on the moving electrons (which is upward, equal and opposite to the magnetic force)
The Hall Electric Field & EMF• The EH is called the Hall Field, after E. H. Hall, who
discovered this effect in 1879
• The EMF produced by the Hall Field is then:
where d is the width of the conductor
• The magnitude of the Hall EMF is proportional to the strength of the magnetic field
BeveE dH
BvE dH
BdvdE dHH
Hall Effect Applications
• A Hall Effect Probe can be constructed to measure the strength of a magnetic field
• A Hall Effect device can also be used to measure the drift velocity, given a known magnetic field