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