Download AdamErickson - Physics - Case Western Reserve University

Solving Non-Intuitive Problems in E&M
Adam Erickson, Research Advisor: Mano Singham
Department of Physics, Case Western Reserve University
ABSTRACT
We analyzed the problem-solving strategies of individuals with varying experience in physics in a conceptually difficult question. An extremely simple direct current circuit with a
qualitative question concerning its flow of energy was presented to novice, intermediate, and expert problem solvers. The results indicate that many students are inclined to think energy
flows through the wires, and is carried by current. Intermediate problem solvers (upperclassmen Physics majors) were able to recognize their incorrect preconception and offer alternative
solutions. This contrasted with introductory-level students who could not expand on other possible solutions when made aware their initial ideas were incorrect. Expert problem solvers
consisted of physics professor. They proved to not only offer the most knowledge on the topic of energy in E&M, but also demonstrated superior problem solving skills. This investigation
covers the key features of the responses of the three groups, which leads to a marked improvement as we move along the spectrum of novice to expert problem solvers.
BACKGROUND
Lillian McDermott conducted extensive research on
misconceptions in E&M, however energy flow in DC
circuits was never investigated. We have modeled an
exploratory experiment after Chandralekha Singh’s
research of a nonintuitive mechanics question that was
answered by Physics professors and introductory
students..
We posed a conceptually difficult question to three
groups, novice, intermediate, and expert problem
solvers. They were given 10-15 minutes to provide an
answer. Responses were given verbally to best follow
the problem solving strategies.
Areas of interest include how problem solving differs
among novel and expert problem solvers, as well as
quantifying level of understanding energy in E&M among
individuals of various experience in physics.
THE QUESTION
Consider the simple circuit to
the left containing a battery and a
light bulb.
When current is
flowing, the bulb will light up,
emitting energy in the form of heat
and light. Explain qualitatively
how the energy gets from the
battery to the light bulb.
SOLUTION
To determine how the energy is being transferred in
this circuit, the E and B fields must be considered. When
these field are found, the cross product of them can be
taken to find the Poynting vector. The Poynting vector is
defined as the energy per
unit time, per unit area
transported by the E and B
fields. It is quantified as
follows:
1
S
E  B
0
The
cross
product
illustrated in Figure 1.
is
Figure 1: Resulting S vector from
cross product of E and B.
In order to find the orientation of the Poynting vector
throughout this circuit, the E and B fields must be
determine. The orientation of these fields can be seen in
Figure 2. The B field is a consequence of Ampere’s Law.
Since the wires have
resistance, an E field
points along them,
driving the current.
Because there is a
potential drop along
the wire, there is also
an E field just outside
the wire, parallel to
the surface. With the
orientation of these
fields known, the
Figure 2: The circumscribed dots represent the B Poynting vector can
field pointing out of the paper, the circumscribed
now
be
found
crosses represent the B field pointing into the paper.
throughout the circuit.
The Poynting vector results from the cross product of E
and B and is illustrated in Figure 3. In the following figure,
the Poynting vector is outward at the battery, and inward at
the resistor (light bulb), indicating a flow of energy from the
battery to the light bulb. The S vector is radially inward at
the wires representing a flow of energy into the wire equal
to the energy being lost in the wire in the form of heat.
RESULTS
The participants’
quality of responses
showed a marked
improvement as we
moved up in each
group.
The key
characteristic of each
group are outlined
below.
-Intermediates - Intuition led 6 of 7 participants to initially
say the energy was carried by current/flowed in wires. All
discovered the contradiction that results from this from this
statement. In their attempts for alternate solutions, many
approaches were taken. These include looking at the
microscopic level, thinking of the circuit as two levels of
potential energy, and the idea that fields are transporting
energy. From 7 volunteers, 2 offered satisfactory answers.
-Experts - The responses from every professor was
lengthier than the novices. Perhaps this is a sign of
internal questioning, a sign of more advanced problem
solving skills. This was also the only group with
participants that made the use of analogies. The experts
showed both a better approach to problem solving as well
as a greater understanding on the topic of energy in E&M.
These two factors contributed to 4 of 6 participants giving
satisfactory explanations on the path of the energy in the
described circuit.
FUTURE WORK
This was an exploratory project, so one question to
consider is, what changes would be made if I were to
conduct these interviews again. My protocol impacted the
participants’ responses (especially novices). No changes
would be necessary for experts’ interviews. With the
novices however, once the point of interest was reached,
the interview did not progress much further. Perhaps
major editing of the question would be appropriate,
making the question posed to novices less open ended.
IMPLICATIONS FOR FUTURE E&M EDUCATION
Results have shown us that in general students at
the introductory level of E&M have little understanding
on the flow of energy in DC circuits. Is this a problem?
Perhaps not as a very thorough model can be made for
the behavior of DC circuits without directly address
where the energy is. This would also be a difficult
concept to handle when learning basics of E&M.
Figure 3: The Poynting vector is illustrated
here. Note it is outward at the battery and
inward at the resistor (light bulb).
-Novices - Responses were short and one thought long.
All interviews reached a contradiction of constant current
and theory of current carrying the energy. No alternate
solutions were mentioned. Out of 8 total participants, none
offered a satisfactory solution.
ACKNOWLEDGEMENTS
I would like to give a special thanks to Mano
Singham, Prof. Chottiner, Brown, and Singer. Also Prof.
Buxton for generously sacrificing both class time and
extra credit. Many thanks also to all the participants who
volunteered their time to answer the question. Without
their time this project would not have been possible.