Purpose
Introduction
to Magnetic Fields and Electrons
Methods
and Qualitative Observations
Magnetic Field Pattern
Earth's Magnetic Field
"Dip" Angle
Cow Magnet
Magnetic Deflection of Electrons
CRT instrument
Helmholtz Coils
Quantitative Analysis Methods
Results
for Quantitative Analysis
Discussion
The purpose of this laboratory exercise in physics II class was to:
There
are a few things that we must understand about magnets before continuing
on with the experimental set-up and results. The first basic concept
is that all magnets consist of a north and a south pole. This is
related with how the magnetic fibers are oriented. The north end
of a magnet is attracted to the south end of a second magnet and vice versa.
However, the north end of a magnet will repel the north end of another
magnet (this is also true for two south poles). If you tried to push
two magnets together with the north ends facing each other (or the south
ends facing each other) the magnetic fields will push on and repel each
other. This results in a space between the two magnets. On
the other hand if you put two magnets together with the north end facing
the south end the magnets will attract each other and "stick" together
will a relatively strong force.
We can also understand that the polarity of a magnet is endless.
You can continuously cut a magnet in half over and over; the resulting
magnets will all have a north and south pole. The poles are
never lost and you will always end with complete magnets (smaller of course!).
Lastly, we must understand that the north end of a compass corresponds
to the north pole of a magnet, and vice versa. Therefore, it can
be predicted that the north end of a magnet would attract the south end
of a compass (similar to the way it would behave with another magnet).
Magnetic Field Patterns (qualitative):
We started off this lab by placing a double-length bar magnet (two magnets
placed together to form a single, long, and straight magnet) under an overhead
projector transparency. We then sprinkled iron filings on top of
the transparency in order to observe the resulting magnetic field.
There is a single large magnetic field around the two connected magnets
that extend out from the general regions of the north to the south poles.
This observed phenomenon can be seen in the below figure:
Second, we seperated the single magnet into two smaller magnets (each having a north and south pole). We then placed these two magnets (with the north pole of the first magnet facing the south pole of the second) at a distance from each other that would prevent them from attaching. We sprinkled iron filings over the transparency covering the two magnets and observed the resulting fields. We found that by breaking the two magnets apart, the result was three separate magnetic fields. There was a magnetic field for each individual magnet between the north and south poles (as seen in Figure One), and there was a third magnetic field in between the two magnets (due to one magnet's north pole facing the second magnet's south pole). This phenomenon can be seen in the below figure:
Figure
Two: Double Magnet Phenomenon
Earth's Magnetic Field (qualitative):
Understanding
that the north end of a magnet attracts the south end of a compass and
vice versa, we were able to understand that the north pole of the earth
is the south end of a bar magnet. Thus, we can interprete this concept
as the compass essentially serves as a spinning bar magnet. We then
simulated the magnetic field of the earth, by using the above method of
placing a transparency over a circular cardboard disk (which simulates
the earth) covering a bar magnet beneath. Iron filings were then
sprinkled on top of the overhead sheet and a magnetic field was observed
radiating out from all points of the earth (NOT just the north and south
poles). So, in truth, we can understand that the magnetic fields
radiate away from the earth at all places on the earth's surface, and not
just out from the poles. This phenomenon can be seen in the below
figure:
Figure
Three: Earth's Magnetic Fields
With regard to using compasses, there is an extenuating circumstance.
It must be recognized that a compass needle only points in the horizontal
component. However, it must be understood that the true magnetic
field of the earth is pointing downward into the earth's surface at an
angle of 45o from the compass needle (at our position in North
Carolina). This 45o angle is known as the "dip angle".
The "dip angle" changes drastically with the latitude on the earth.
It is about 45o at mid-latitudes, but it is zero at the equator
and near 90o at the poles. This "dip angle" can be measured
using a special compass that is gravitationally balanced. However,
because it is so difficult to balance these needles, the compass information
is usually unsatisfactory and inaccurate.
Another interesting demonstration we performed in lab involved the cow
magnet. This is a very strong magnet that is force-fed to cows to
attract any nails or other iron metal objects the cow may have ingested.
The magnet does not attract zinc, copper, or other non-magnetic metals.
This magnet then allows the cow to pass these magnetic objects through
it's intestines thus preventing any illness from occurring due to these
ingested metals. In lab, we placed the cow magnet in a capped test
tube, which was then submersed into a suspension of iron filings in paraffin
oil. From this demonstration, we were able to observe the three-dimensional
magnetic fields created by the round cow magnet. These 3-D fields
go out in all planes similar to the magnetic fields created by the earth's
core.
Magnetic Deflection of Electrons (qualitative):
We began by constructing an apparatus that would allow us to observe the
correlation between magnetic fields and electrical currents. A diagram
of this apparatus is shown in the below Figure:
Figure
Four: Electrical Current and Magnetic Fields Apparatus
We
began with the four compasses facing North. We then ran a "large"
current through the wires and found that when the current ran up, the compasses
all pointed in a counterclockwise direction around the wire. The
current was then reversed and we observed that with the current going down,
the compasses all pointed in a clockwise direction around the wire.
This relates to the deflection of the compass needle due to the current
of electrons relative to the position of the compass around the wire.
This correlation is what forms the observed clockwise/counterclockwise
pattern. The magnetic field is rotating around the wire and it has
a circular pattern, resulting in the four compasses forming a visual of
this circular pattern in the direction of the magnetic field.
We then made a self-supported coil out of three meters of hook-up wire
and attached this coil to a hand-cranked generator. We placed the
coil vertical running along the North and South axis, and we placed the
compass inside the coil at a perpendicular position pointing North.
A diagram illustrating this is shown in the below figure: (the red
dotted lines indicate the magnetic fields)
Figure
Five: Magnetic Fields Around A Wire
When the generator is cranked one way, the compass points East; when the generator is cranked in the other direction, the compass points West. This phenomenon is due to the fact that the magnetic field is going around the coil and is perpendicular to the wire. So, when the current is going to the left, the magnetic field is moving counterclockwise, and when the current is going to the right, the magnetic field is moving clockwise. However, the clockwise or counterclockwise direction can change depending on the observer. So direction can be determined using the "Right-Hand Rule". This rule incorporates the observer pointing their thumb in the direction of the current and the direction in which your fingers on your right hand wrap around your thumb is the way the magnetic field wraps around the wire. The compasses deflect due to the direction in which the magnetic field is directed.
CRT instrument and deflection of electrons (qualitative):
The CRT is an instrument which gives off a small light created by a beam
of electrons moving at a high velocity. With a permanent magnet held
above the machine and the North pole pointing down, the beam of electrons
is deflected to the left; with the South pole pointing down the beam of
electrons is deflected to the right. This deflection of electrons
is due to the electromagnetic force. The electromagnetic force (EMF)
on electrons is perpendicular to the electron's velocity as well as to
the magnetic field. Therefore, if the electron's velocity is to the
right and the magnetic field is pointing upwards, then the EMF is pointing
directly away from you (into the plane of the paper). On the other
hand, if the electron's velocity is to the right and the magnetic field
is pointing downwards the EMF is pointing towards you (out of the plane
of the paper). This is what is known as the "Left-Hand Rule".
You point your left hand straight out from your body and you bend your
four fingers up or down as corresponding to the direction of the magnetic
field; the resulting direction in whch your thumb points is the direction
of the EMF force.
When we placed the magnetic field horizontal to the beam of electrons we
found that the North pole of the magnet resulted in the beam of electrons
being deflected up. The South pole of the magnet resulted in the
beam of electrons being deflected down.
We then used the CRT instrument with the hand generator and coil to observe
how the current deflects the beam of electrons. We found that with
a counterclockwise current the magnetic field is going up and the EMF is
perpendicular to the electron's velocity and the magnetic field.
When we cranked the generator back and forth we could see the electron
beam move right and left or up and down accordingly with the position of
the coil. We can also observe that a higher current increases the
magnetic field, so with the larger coil (with a different geometric arrangement
from the hook-up wire) and the hand generator we observe a much larger
left and right effect. This coil has much more turns than the hook
up wire, so there is a much larger magnetic field. Each turn in the
coil produces a small amount of a magnetic field, so as the number of turns
increases the magnetic field increases proportionally. It is also
understood that the transformers in the power supply have a magnetic field
as well resulting in leakage. Therefore, if we crank the hand generator
really fast, we can observe an oscilloscope effect with the electron beam
creating a wave pattern.
We then connected the Helmholtz coils in a series and placed a compass
in between the coils. We cranked the hand-generator to create a current
and discover the effect of the Helmholtz coils on the magnetic fields present.
We found that the magnetic field in between the coils is not as strong
as at each individual coil, but the magnetic field is uniform. Below
is a diagram illustrating the magnetic fields around a single coil:
Figure
Six: Single Coil
However, with two coils, the magnetic field dips in slightly in between the two coils as illustrated in Figure Seven (below):
Figure
Seven: Helmholtz Series
Quantitative Analysis Methods:
The quantitative section of our lab involved the students setting up a
quantitative apparatus for the magnetic deflection of electrons with the
TEL 525 electron tube. This vaccum tube is equipped with an electron
"gun" which shoots electrons towards a graticle screen tilted at an angle
that makes the electron path visible. When a magnetic field is applied
to the tube the electron beam can be deflected. We found that with
the current moving in one direction, the electron beam was deflected upwards;
and when the current direction was switched the electron beam was deflected
downwards. We also found that by decreasing the energy or the voltage
this resulted in the electrons traveling slower and the beam being deflected
or bent even further.
We then for several voltages between 3,000V to 4,600V, adjusted the Helmholts
current so that the beam passes through the coordinates (12cm +/-
2.4cm) and calculated the average of the two coil currents (+I,-I).
We used the average current, the radius of the coil (0.068cm), and the
concept that there are 320 turns (n) in the Helmholts coil to calculate
the average magnetic field using the equation: B=[(8.99*10-7)*(n/a)]*Iaverage.
This value was then used to calculate the e/m ratio, using the radius of
the electron's orbit (0.301m), the voltage, and the magnetic field.
Both the magnetic field and the e/m ratio were calculated for all nine
data points.
Results
for Quantitative Analysis:
All of the calculated values for the magnetic fields and the e/m ratios are shown in the below table:
Table One: Voltage, Average Current, Magnetic Fields, and E/M
| Voltage (V) | Average Current (Amperes) | Magnetic Field (N/amp*m) | E/M |
| 3,000 | 0.187 | 0.000791 | 1.058*1011 |
| 3,200 | 0.195 | 0.000825 | 1.038*1011 |
| 3,400 | 0.199 | 0.000842 | 1.059*1011 |
| 3,600 | 0.204 | 0.000863 | 1.067*1011 |
| 3,800 | 0.210 | 0.000888 | 1.063*1011 |
| 4,000 | 0.215 | 0.000910 | 1.067*1011 |
| 4,200 | 0.221 | 0.000935 | 1.061*1011 |
| 4,400 | 0.227 | 0.000960 | 1.053*1011 |
| 4,600 | 0.232 | 0.000981 | 1.054*1011 |
The average e/m ratio for all nine observation values was found to be 1.056 * 1011 and the literature value for the e/m ratio was determined to be 1.76 * 1011. The percent error was determined to be 40%.
The experimental error of 40% is extremely high; however, it is believed
that this was due to a large systematic error in the experiment.
This means that there was very good precision in our experiment (very little
experimental data scatter), but the accuracy of our data was bad.
The magnetic field formula is for the center of the two coils, and it assumes
that the magnetic field is constant. However, in the coil used in
this experiment, the magnetic field is smaller at the start and end of
the electron beam than in the middle of the beam. The book value
is based on experimental data from experiments using coils with a much
larger diameter, giving the researcher a more accurate value.
Links
to More Sites:(concerning Magnetism)