Download Charges in a Magnetic Field

Charges in a
Magnetic Field
An electron entering a magnetic field experiences a
force similar to that on a wire. A proton would
experience a force in the opposite direction.
Since we have F = IlB,
and I = q ,
t
then we can substitute so we get
F = qlB ,
t
and
l =v
t
Then, the force on a proton or electron, or any
charged particle is:
F = qvB
Practice Problem:
What is the force on a proton moving at 2.0 x 106 m/s
in a magnetic field of 0.5 Tesla.
F = qvB
q = 1.6 x 10-19 C
v = 2.0 x 106 m/s
B = 0.5 T
F = (1.6 x 10-19 C)(2.0 x 106 m/s)(0.5T)
F = 1.6 x 10-13 N
Since a particle is free to move, upon entering a
magnetic field, it will constantly change directions in
response to the force, and it moves in a circle.
proton
+
electron
Magnetic field out of page
Mass Spectrometry
A practical application of this, is a device known as a
mass spectrometer, which uses the charge to mass
ratio of ions to determine the masses of particles.
By measuring the speed of the particles and the
radius of the path, we can use
F = qvB , and, Fc = mv2
r
then,
qvB = mv2
r
And we get,
q = v
m Br
If the charge on the particle is known, the mass can
be calculated.
A Little History
• In 1897, J.J. Thomson found the charge to
mass ration (q/m) for an electron.
• Between 1909-1913, Robert Millikin found the
charge for an electron using his oil drop
experiment.
• From this charge, the mass of the electron
could be calculated
using Thomson’s ratio.
Electron Beams
An electron beam can be created through thermionic
emission. An electron beam is generated when a
filament is heated until it emits electrons.
Once they are
emitted, the
electrons are
controlled by
electric and
magnetic
fields.
Devices such as computer monitors, television tubes,
and cathode ray tubes create electron beams.
A cathode ray tube is
an evacuated glass
tube with an electron
source at one end, a
screen at the other,
and controlling plates
and magnets in
between.