Download Exercise 4

Astronomy 102
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Exercise 4: 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. 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?
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N
4. As best as you can, draw the magnetic field lines on your sketch. What pattern
does this resemble (think back to Exercise 1)?
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?