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Mapping the Magnetic Field
Mapping the Magnetic Field
Vector Fields
~ and the magnetic field, B,
~ are
The electric field, E,
two examples of what are termed vector fields,
quantities which have both magnitude and direction
(hence are vectors) that can be assigned to every
point in a region of space. When you studied the
electric field you learned that the magnitude of the
field at a point was related to the amount of electric
force experienced by an electric charge located
somewhere in the field. The direction of the field was
given by the direction of the force (if the charge was
positive). The magnetic field is defined in a similar
fashion, in terms of the magnitude and direction of a
force an (hypothetical) isolated magnetic element.
Measurement of the electric field, in a quantitative manner, is rather difficult. Nearby materials,
including the humidity in the air and even you,
the experimenter, can distort the measurements.
Fortunately, measurements of the magnetic field
aren’t nearly so difficult. The instrument needed
to determine the direction of the field is a simple
compass. Determining the magnitude is a bit more
of a challenge. The advantage is that only nearby
magnetic materials (iron, steel, etc.) will significantly
distort the field. It is reasonably easy to arrange
an experimental space free enough of these kinds of
materials to permit good measurements.
One agent of distortion is not so easy to eliminate—the magnetic field of the Earth itself. It is possible to
produce localized magnetic fields that, at least within a limited region of space, are much stronger than the
Earth’s field such that the distortion is minimized. We can also use the Earth’s field as a sort of comparison
standard, measuring the strength of a given magnetic field in comparison (ratio) to that of the Earth.
Direction of the magnetic field
Magnetic elements (poles) appear in pairs, labeled north poles and south poles. When a magnet (which
possess a north and a south pole on opposite ends) is suspended and allowed to swing freely, it will align
itself with the Earth’s magnetic field in such a way that the north pole of the magnet points generally in a
northerly geographic direction. Similarly to electrostatics, in magnetism opposites attract, and this means
that somewhere near the North Geographic Pole (where Santa lives) is located a South Geomagnetic Pole.
The actual position of the geomagnetic pole in the northern hemisphere is somewhere in the vicinity of
Hudson Bay, in Canada. The location is not constant, and there is a slow drift over the years. In fact the
poles periodically reverse direction, but the next reversal is not expected for thousands of years, so don’t
throw away your compass yet.
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By agreement, scientists define the direction of a magnetic field as being in the direction of the force that
would be exerted on a north magnetic pole located in the field. This means that the direction of the field
is very easily found by noting the direction that the south seeking end (usually marked in red, or with an
arrowhead) of a compass points. If you put your compass near the north magnetic pole of your bar magnet
(marked with the N), the north seeking end of the compass points away from the pole. If you put your
compass near the south magnetic pole of your bar magnet (marked with the S), the north seeking pole of
the compass points toward the pole. As a result, magnetic field lines should point away from magnetic
north poles and toward magnetic south poles.
In today’s experiment you will use a small compass to
map the direction of the magnetic field in a plane region surrounding one or more permanent bar magnets.
You will also investigate the magnetic field produced
by a coil of wire in which a steady current is flowing.
Notice in the figure at right how the grey (north seeking) end of the compass points towards the south pole
of the bar magnet. At every position in the vicinity of
the magnet the compass indicates the unique direction
of the net magnetic field vector at that point. Remember that what is represented is actually the vector sum
of the magnetic field vector of the bar magnet and the
magnetic field vector of the Earth. Close to the magnet
its field is much stronger than the Earth’s, and Earth’s
contribution is negligible. Farther away the Earth will contribute a significant, or perhaps even predominant
part of the net field.
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Mapping the Magnetic Field
APPARATUS two bar magnets, DC power supply & leads, large copper wire coil, compass, 11 × 17 inch
paper, straight pins or pushpins, sticky tape
PROCEDURE
First clear away from the table top any magnets or iron or steel objects. Place your compass in the middle
of the table and determine the direction of north. In your classroom (Rooms 14 and 16 of Nicholson Hall)
north is approximately opposite the windows. The steel in the building structure may cause your compass
to point in a slightly different direction.
Stack on top of one another one of the large sheets of
paper for each person in your lab group (i.e., for you
and one partner, stack two sheets). Put a bar magnet
on top of the sheets, orienting the bar magnet so that
its long dimension runs north-south. Turn the paper so
that its long dimension is roughly perpendicular to the
long dimension of the magnet. Look at the figure for
clarification. It doesn’t really matter which end of the bar
magnet is towards the north, pick either orientation you
like.
Use some tape to secure the paper to the table, and trace
the outline of the bar magnet with a pen or pencil. Identify
(using your compass) which end of the bar magnet is the
north pole. (Don’t trust any markings on the magnet, they
have been known to be incorrect. Label on your paper which is the north pole of the magnet.
Now use your compass to create a map of the magnetic field lines around the magnet. Do this by placing
the compass in a starting point (several suggested starting points are shown in the figure as dots), and
turning the compass until the needle lines up with the two holes in the base. One it’s aligned, stick a
pencil into each hole and make a dot. Move the compass to one side or the other, but arrange it so one
of the holes in the base is directly over one of your pencil dots. Align the needle with the holes and make
another pencil dot. Continue this process in both directions to complete the field line. You might wish to
connect the dots as you go along, or wait till later. In either case, when you do connect the dots, use an
arrowhead to indicate the direction that the north (red) needle of the compass was pointing. Begin again at
another convenient starting point and repeat the mapping process several times until you have traced out a
few (need not be more than five or so) lines on each side of the magnet and a two or three lines near each end.
To allow both you and your partner(s) to have a copy of the field map, use a push pin and poke through
the paper at each pencil dot so that you prick the sheet(s) below. This will allow an accurate copy of the
original map to be produced.
After you’ve done the first map, obtain some fresh sheets of paper and map another case where you orient
the bar magnet in an east-west direction, again keeping the long dimension of the paper perpendicular to
the long dimension of the magnet.
Make two more field maps of the region in between the poles of two separate bar magnets. Try each of the
orientations shown in the figure below. Trace six or more lines spaced across the region of the facing poles.
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Use a fresh stack of paper for each case.
Case 1: Unlike Poles
Case 2: Like Poles
Finally, use your compass to investigate the magnetic field produced by a coil of wire carrying a steady (DC)
current. You will not actually trace the fields on paper this time, just observe carefully so that you can
describe what you saw.
Connect a DC power supply to one of the large (3400 turns) coils as shown in the figure. Leave the power
supply turned OFF until your instructor has checked your wiring for accuracy. Once your wiring is checked
and is correct, turn ON the power supply.
You can move the compass around, above, and even inside the coil to see which direction the magnetic field
points. While holding the compass in a given position, have your partner reverse the connection at the
power supply and observe the effect. Try varying the voltage output of the power supply (which controls
the current flowing in the coil. Again, observe any effects.
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ANALYSIS
Questions 1 through 3 pertain to the single magnet case.
1. Was there anything about the behavior of the compass that would give some indication of the magnitude
of the field at the location of the compass?
2. Examine your field maps. Is there a relationship between how closely spaced the lines are and how
strong the field (magnitude) is?
3. Did it appear that any of the field lines would cross over one another? Explain why.
Question 4 pertains to the two-magnet cases.
4. Describe the difference between the like-pole and unlike-pole field maps.
Questions 5 through 8 pertain to the coil.
5. Describe, perhaps including a rough sketch, the field around the coil. How about inside the coil. How
did the appearance of the field near the coil compare to the field near a single bar magnet? Could you
identify a “north end” and a “south end” of the coil?
6. Explain how the “right hand rule” can predict the direction of the field inside the coil. (You may need
to refer to your physics text.)
7. What happened when the power supply was reversed? Why?
8. What happened when the power supply voltage was varied? Why? Did the distance from the coil
matter?
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