Download Unit 4 Day 4 – Electron Properties & Hall Effect

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
Evacuated but
back filled with
rarified gas
• What was emitted & observed as a “glow” was called
cathode rays. It was later determined that these were
ionized electrons.
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 BField is applied, the electrons curve down.
v2
e
v
evB  me
or

r
me Br
Electron Properties
• Remember, in previous experiments performed by J. J.
Thompson, if the Electric and Magnetic forces are
balanced:
eE  evB
or
• The electron velocity becomes:
E
v
B
E
e
v
E

 B  2  1.76  1011 kgC
me Br Br B r
• E, B, & r, were all measurable quantities
Electron Properties
• Note: In later experiments
by Millikan (Oil-drop Experiment),
the charge of the electron was
established.
eE  mdrop g
e
mdrop g
E
 1.602  1019 C
• Knowing e and e/me, then me was calculated to be:
me  9.11  1031 kg
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:
FB  evd  B
where vd = drift velocity
• The electron will tend to move to the bottom of the
conductor (D)
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
eEH  evd B
 EH  vd B
• The EMF produced by the Hall Field is then:
 H  EH  d  vd Bd
where d is the width of the conductor
• The magnitude of the Hall EMF is proportional to the
strength of the magnetic field
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