Download The Movement of Charged Particles in a Magnetic Field

The Movement
of
Charged Particles
in a
Magnetic Field
By
Emily Nash
And
Harrison Gray
• Magnetic fields and their poles
• Magnetic field of the earth
• Solar wind and how the earth’s magnetic
field affects it
• Taking a look at the force that magnetic
fields exert upon electrons by using a
cathode ray tube, magnets, and some
simple math.
Magnetic Fields are
created by moving
charged particles,
and only affect
moving
charged particles.
When there exists a
steady
stream of electrons,
a negatively
charged particle, an
electric
current forms,
which produces
a magnetic field.
N
S
Forces between two
electric currents is
what causes a
magnetic force. Two
parallel currents
flowing in the same
direction repel each
other, while two
parallel currents
flowing in opposite
directions repel each
other.
This force leads to
the idea of the north
and south poles of
a magnetic field.
The Earth itself is a magnet, with a magnetic north
pole and south pole.
N
S
The origin of the Earth’s magnetic field is
said to be a result of the dynamo effect,
electric currents produced by the rotation
of the iron-nickel core.
The Earth’s magnetic field
continually traps moving
charged particles coming from
the sun.
High concentrations of these particles within the field
are called the Van Allen Radiation belts.
These particles are called cosmic rays, which originally come from the sun.
Magnetotail
Solar Wind consists of gases comprised
of protons, electrons, and ions which
hurl towards the earth from the sun at
velocities of 450 km/sec or higher.
Bow Shock
The path of these particles change almost
directly as they hit the earth’s
magnetosphere at the region called the bow
shock.
Magnetosheath
The impact of the solar wind causes
The field lines facing the sun to compress,
While the field lines on the other side stream back to form a
Magnetotail.
Because the charged particles of the rays are
deflected around the magnetosheath,
the earth is protected from most of the deadly
radiation.
Some solar wind particles, however, do escape the earth’s magnetosphere and
contribute to the Van Allen radiation belts.
When these particles do enter the magnetic field, they go through three motions:
• Spiral- the magnetic field changes the path of the particle. The particle, in its
new path, is still deflected by the field, and therefore takes a spiraling motion
around a magnetic field line.
• Bounce- the particles eventually bounce towards the opposite pole, where they
spiral again.
• Drift- as the particle continually spirals and bounces, it drift around the magnetic
field and is trapped in the magnetosphere.
In order to better understand the motion of particles through a magnetic field,
we have conducted an experiment involving creating an electron beam and
running it through magnets as a parallel to solar wind entering the earth’s
magnetic field.
√
The potential energy
of electrons is converted
to kinetic energy
Since change in energy is the
Electrons
aretimes
attracted
to positively charged
voltage
the charge
plate.then
They½mv²=qV
accelerate towards it and small
percentage
escape
the plate through small
Therefore
v= √(2qV/m)
hole, creating electron beam.
120 Volts
Plate is heated and
electrons boil off.
Velocity= 0
Potential Energy= ½ mv^2
6.3 Volts
We now know that v= √(2qV/m), so we can now easily find the
velocity of our beam of electrons.
q(charge) of an electron= -1.6•10^-19
V(volts)=120
m(mass) of an electron=9.11•10^-31
Therefore:
v=√(2)(-1.6•10^-19)(120)/(9.11•10^-31)
v=√4.215•10^13
v=6492417.261 m/s
Like Solar Wind,
the electrons in the
CRT beam are
deflected
when entering a
magnetic field,
therefore the
electron
beam “bends.”
Since acceleration
is equal to v²/r
we can deduce that
F=m(v²/r)
In order to predict
the angle at which
the electrons are
deflected, we must
first measure
the force that the
magnetic field inserts
upon the beam
To do this, we use the equation:
F=ma
according to Newton’s second law
We now know that F=m(v²/r), so we can use this formula to find the force
that the magnetic field exerts upon the electrons.
mass= 9.11•10^-31
velocity= 6492417.261 m/s
And we measured the distance of the electron beam from the magnets
to be .075 meters
Therefore F= 9.11•10^-31(6492417.261²/.075)