Download Lab 4, part one

Astronomy 102
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Lab 4, part one: Electric and magnetic fields
Learning outcome: Ultimately, to understand how a changing electric field
induces a magnetic field, and how a changing magnetic field induces an electric
field, and how both are aspects of electromagnetic radiation.
Electromagnetic radiation, as we’ve seen in previous exercises, is pervasive. Yet
until the middle of the 19th century, physicists widely believed that EM waves
could exist in a vacuum. Further, they did not connect EM waves to light, even
though some of them suspected that there would be a connection.
The magnetic field of a coil of current-carrying wire
Equipment needed: a coil of wire, a power supply, the Labquest data loggers with
magnetic field strength detectors, a set of small compasses
In 1819, Hans Oersted did a demonstration for his graduate students, trying to
show that a current in a wire generated a magnetic field; to detect the magnetic
field, he held a compass near the wire. At first, his demonstration failed, but then
he had the insight to change the orientation of his compass, and the needle
turned in response to the current; when he reversed the current flow direction,
the needle of the compass turned the other way.
Ampère’s Law (Maxwell Equation 4) states that an electric current generates a
magnetic field, and this exercise will illustrate that point.
First, set up the coil and power supply in the middle of the room; if possible, keep
the coil upright, but you can lay the coil flat. Don’t connect the power supply yet.
Array the compasses such that they are scattered inside and outside the coil at
differing distances from the coil..
1. On the next page, sketch the floor plan of the room, indicating where the coil is,
and how it is oriented. The instructor will show you which way north is in the
room, though the compasses should make that pretty obvious!
Turn on the power supply.
2. Show, on your sketch, the orientation of the needles of each compass (use a
different color pen or pencil to show the change). Try to make the orientations as
accurate as possible, so that you can tell if the needle orientation is only a little
affected, or if it is affected a lot.
Turn off the power supply.
3. Calibrate all of the Labquest dataloggers and the magnetic field strength
detectors by making sure they get the same reading for the terrestrial magnetic
field strength. Place a detector near every spot where there is a compass. Turn on
the power supply, and note, on the sketch, the value of the magnetic field
strength. Do the magnetic field strengths correspond well with the amount of
deflection on the compass needles?
↑
N
4. As best as you can, draw the magnetic field lines on your sketch. Draw arrows
pointing towards the north pole on each line; if there are lines only connected to
the south pole, draw an arrow going away from the south pole. What pattern does
this resemble (think back to Lab 1)?
5. Draw a circle around either pole in your sketch; it should cross a number of
magnetic field lines. The flux of the magnetic field is calculated by counting all
the field lines that cross the circle that are pointing toward the pole and
subtracting the number of field lines pointing away from the pole. What is the
flux around the pole you have chosen? If you had chosen to draw the circle in an
area far away from either pole, would the flux have been larger or smaller?
The ring launcher
Equipment needed: ring launcher, a set of different mass and material rings, a
field extender, and an electronic balance
In 1865, James Clerk Maxwell published an article titled “A Dynamical Theory of
the Electromagnetic Field” in the Philosophical Transactions of the Royal
Society of London. In the article, he described a set of equations that unified the
until-then separate forces of electricity and magnetism as one force called
electromagnetism. Eventually, his equations were distilled into the four
Maxwell’s Equations of Electromagnetism. Because the phenomena were
discovered long before Maxwell’s time, the individual equations are known by
other scientists’ names.
In particular, Faraday’s Law (Maxwell Equation 3) suggests that a changing
magnetic field induces an electric field. If there is a conductive material, like a
wire, in the field, an electric current will be set up in the material.
A good illustration of these principles is found in the ring launcher. The launcher
is simply a coil of wire attached to an electrical cord – when plugged into the wall
socket, the alternating current (AC) of a standard building power supply will
generate an alternating direction electric current in the coil, which in turn will
generate an alternating direction magnetic field within the coil and an alternating
direction electric current and magnetic field in any ring of material placed around
the coil. The two magnetic fields (inside the coil and inside the ring of material)
will repel and move the ring up.
Actually, the generation of force is still not that well explained; check out a recent
attempt at explanation by a physics professor:
http://www.wired.com/wiredscience/2014/01/physics-of-the-electromagneticring-launcher/
This doesn’t mean that we can’t at least discover some empirical relationships
about the force that propels.
5. Place the coil attached to the bulb circuit on the ring launcher and briefly turn
on the launcher. What happened to the bulb? Explain this phenomenon, using
the word “induction” or “induced”.
6. Now carefully launch (or attempt to launch) various rings of different materials
and sizes. Record the information in the table below; with the height the ring
goes up, you can be approximate.
Ring material
Ring height
(cm)
Ring mass (g)
Maximum
movement height
(cm)
The rings are all machined to be the same thickness and diameter, so when a ring
is double the mass of another ring of the same material, it is twice the height of
the other ring.
7. The conductivity of a ring depends on the area though which the current will
move – for the rings, the area is the inside of the ring. So if one ring is twice the
mass of another ring of the same material, what can be said about the ring’s area
(compared to the other ring’s area)?
8. So what is the mathematical relationship between ring height and ring
conductivity, roughly?
9. Test this theory: copper has about twice the conductivity of aluminum. Look
at the data for the aluminum and copper rings of the same height. Which would
you predict would have a greater maximum movement height, and why? Was
your prediction true? How confident are you about the ring height/conductivity
connection in part b?
10. How did the “split” ring do? Explain the result in terms of Maxwell’s
Equations.
11. Place the iron core snugly in the middle of the coil, then launch a ring.
Record the maximum movement height in centimeters and compare this number
to the movement height of the same ring without the iron core. Why does the iron
core improve the maximum movement height?
The non-existence of magnetic monopoles
Gauss’s Law for Magnetic Fields (Maxwell Equation 2) states that there can be no
magnet with only one pole (a monopole). Another way to state this is the flux
from any magnet must equal zero (since it has both a north and a south pole).
You’ll measure this by using the magnetic field sensor from Lab 1.
Needed:
• magnetic field sensor
• Labquest data logger
• three-fingered clamp and a ringstand
• meter stick (maybe two of these)
• cylindrical rare-earth magnet
Attach the three-fingered clamp to the ringstand about six inches above the base
of the stand. Clamp the magnetic field sensor and adjust it so that the sensor is
horizontal and the “white dot” (the sensor itself) is pointing downwards. Connect
the sensor to the data logger, and make sure the Earth’s magnetic field is being
detected.
Place the magnet on one of its flat sides on top of a meter stick at a convenient
graduation (mark). This will be your zero cm point. Choose a positive and
negative direction for distance measurements along the meter stick (that is, one
direction away from the magnet should be increasing positive distances; the other
direction should be increasing negative distances).
Place the meter stick with the magnet onto the ringstand base such that the
magnet is positioned under the magnet. Get the largest absolute value of the
magnetic field possible, and this will be your start point.
• Remember, the sensor has a maximum value it can read, so adjust the height of
the sensor higher if you max out the sensor.
• Remember, also, that the Earth’s magnetic field is a minimum value; if this is
the maximum value you obtain from the magnet when it is under the sensor,
adjust the height of the sensor lower.
12. On the next page is a table of measurements of magnetic field strength you
will take at various distances, both positive and negative, from the start point.
You will adjust the distance by sliding the meter stick along the positive or
negative direction until the desired distance is achieved. One way to keep track of
how much you have moved is to keep another meter stick next to the one with the
magnet, and don’t move that one while the magnet meter stick moves; this way,
you can figure out the distance.
The “+ infinity” and the “– infinity” distances indicate a sufficiently far distance
that you are certain you are detecting only the Earth’s magnetic field; do record
this field strength as well!
To calculate the corrected magnetic field strength, simply subtract the Earth’s
magnetic field strength you recorded at one of the “infinite” distances from the
magnetic field strength at that distance.
When you are done with all of the measurements, flip over the magnet and remeasure all the distances in the other set of columns provided.
Original orientation of magnet Flipped orientation of magnet
Distance (cm) Magnetic field Corrected
Magnetic field Corrected
strength (mT) mag. Field
strength (mT) mag. Field
strength (mT)
strength (mT)
0
+1
+2
+3
+5
+ infinity
–1
–2
–3
–5
– infinity
total
13. Sum all of the “corrected magnetic field strengths” in the original orientation
of the magnet, and enter that into the “total” cell on the table. Do the same for the
flipped orientation of the magnet. One of these numbers may be negative; that’s
okay.
14. Sum the two “total” numbers – what do you get? If, instead of milliTesla, you
think of the magnetic field strength as a measure of flux (the number and
orientation of magnetic field lines), argue whether you have a magnetic
monopole or a magnetic dipole.