Many are familiar with the Field Mapper from Pasco, or with its
equivalent. Two spots of silver, for example, two dots or two
parallel lines, are painted on a sheet of carbon impregnated and
connected to a d.c. source. One spot becomes positive and another
becomes negative, like in a dipole or in a capacitor. Potentials, for
example, with respect to the negative terminal, are then measured
in different locations of the sheet. Students sketch equipotential
lines and field lines which are perpendicular to them.
The patterns of lines are the same as in electrostatic fields but
the situations are not electrostatic. What is drawn as an E line
is actually the current density line. I think it is a very good
activity, even if its true nature is not immediately obvious to
students. I was playing with this setup and found an unusual set
of lines. Others have probably explored this but as far as I am
concerned it is an “original” expariment.
1) It started by performing a standard student experiment for
a dipole field. Two silver dots (each about 5 mm diameter) were
18 cm apart on my paper sheet. The 10 megaohm Simpson digital
voltmeter was used and the pattern of line was as expected.
The dot locations were (5,10) and (23,10); the cm coordinates
are printed on the paper.
2) Next a line segment of 18 cm was silver-pained to connect
the two dots. This produced a metallic strip whose resistance
turned out to be 21 ohms (instead of about 40,000 ohms as it
was without the strip). The DOP of 2V was connected to the
strip terminals and the equipotential lines were again determined
using the same voltmeter. First I measure voltages along the
metallic strip at various locations on the paper. The equipotential
lines were turned out to be more or less as in part 1. (It was not
easy to paint a line of nearly uniform resistance; I wasted several
sheets before succeeding.)
3) Now comes the “innovating” part. Another sheet of paper,
as in part 1 was prepared (two silver dots 18 cm apart). The
dots were then connected by a zigzag silver strip.
Segment 1 from (5,10) to (10,16)
Segment 2 from (10,16) to (18,4)
Segment 2 from (18,4) to (23,10)
The total resistance was 23 ohms and the DOP of 2.35 was
applied to the ends of the zigzag strip. The distribution of
potential couln't possibly be the same as it was for a dipole.
That was clear. But what should it be? Unable to answer this
question I decided to map the field again using the same
voltmeter. This generated a topography where the equipotential
lines were no longer perpendicular to metallic segments (they
were perpendicular for a strip without bends in part 2).
For example, after measuring that U=0.79 V at a point on my
strip (at x=14 and y=10 cm) I located several 0.79 V points on
each side of the segment. Their coordinates were
U=0.79 V (9,1), (12,6), (13,8.2), (0.5,3) (0.8,16) and (14,20)
This equipotential line makes an angle of about 35 degrees
with the segment. I have many lines like this. For example,
U=0.54 V at (0,3), (4,4), 10,8), (12,13), (12,16), (11,19).
or a loop around the positive terminal.
U=1.95 V at (26,9), (23,7), (20.5, 6.8), (21,9), (24,11)
This puzzles me. Any comments?
The distribution of R along the strip was not uniform but I do
not think that this can be responsible for what is observed. (For
exanple, the potential in the center of segment 2 was 0.79 V
instead of 1.17 V). Is it not true that equipotential surfaces
in a wire are always perpendicular to the direction of the
current flow? I always tell students that the field in a typical
wire is uniform, for example, 100 V/m, when a one-meter
wire is connected to a source of 100 V. bending a wire does
not change E, presumably. Is this correct. )
I suspect that many of you are using Pasco setup at this time
of the year. Can somebody verify my observations? I know that
this is not an expected use of the field mapper but why should
this prevent us from doing something different? By the way, the
Field Mapper Kit (part PK-9023) costs $99. You will get 100
sheets of special paper, conductive ink pen, wires and pins,
plus the corkboard, plus the instructions. But you must have
a good voltmeter and a d.c. source (a battery or a power
supply). If your old conductive ink pen dried you can order
a new for $17. Call Pasco at: (800)-772-8700.
Ludwik Kowalski