October 13, 2019 Filed in: Articles

Richmond Hill HS (retired)

STEAM Education Consultant, FAST Motion Studios, Toronto

A 2016 paper

The actual mechanism of potential difference and direct current involves surface charge distribution. The challenge to develop this conceptual foundation is its invisible nature. Students cannot directly observe charge and ‘creative instructional design’ is needed to carefully scaffold inferences from static to moving charge. This paper suggests a series of activities to create the experiential background necessary for robust modelling of surface charge distribution. This conceptual foundation will be applied to series and parallel circuits to reinforce Kirchhoff’s laws.

How does understanding surface charge density contribute to equity? According to Carol Dweck

At this point the terms conductor and insulator can also be operationalized. An inflated latex balloon is charged negatively with fur/dry human hair at a location on the balloon. Circle the location with a marker and label as (-). This region is strongly attracted or repelled by the transparent tapes. A rotation of the balloon reveals the charge to be localized, as other regions of the balloon are neutral (or far weaker in charge)

For a conductor, a spherical metal surface is ideal though a flat aluminum pan can substitute. Charge the metal by contact. Rotation of the sphere — held the same distance from the charged tapes — will reveal an equal charge distribution on the spherically symmetric surface, as witnessed by constant attraction or repulsion of the charged tapes. This operationalizes a conductor.

Students need to be encouraged to use words and diagrams to explain the observations on the insulator and conductor (e.g. whiteboarding). However, to try and ensure common visualization, role-playing is invoked. Role-playing allows students to deconstruct and repackage core concepts. In this collaborative environment students discuss and refine terms and concepts, confront misconceptions, and nuance details under-appreciated in a didactic presentation. Multiple representations accommodate students’ different strengths in perception, language, and comprehension.

Provide students with two 8.5 x 11 sheets; one labelled as (+), the other (-). Mark out an area on the floor as a sample of a neutral metal outer surface. Students move onto the surface, placing the (+) page on the floor while holding the (-) page. When students move, the (+) charge remains fixed on the floor, appropriate for fixed nuclei in a conductor. Students assume the role of (-) charge (valence electrons) and are mobile on the outer surface.

Students are asked to distribute themselves in a scientifically-reasonable manner and articulate their reasoning (e.g.: we repel each other so we get as far apart as we can, without bunching up). Avoid providing the ‘right’ answers — allow them to reach consensus, even if errors exist. Use Socratic questioning to help them confront and resolve misapplications. This aids in teaching how to think, not what to think.

Introduce scenarios as appropriate, such as:

- bring a (-) charged insulator near the metal surface and allow students to redistribute. This will operationalize induction as the surface does not gain or lose charge but does now have (+) and (-) regions.
- bring a (+) charged insulator near the metal surface and allow students to redistribute.
- repeat a) and b) but change the neutral metal surface by first removing or adding (-) charge. This starts the paradigm with a charged outer surface interacting with a charged insulator.
- separate students into two adjacent outer metal surfaces. Allow student choice as to the charge state of each metal surface. As before, let them achieve consensus and moderate results as needed.

A charged metal surface is then used. The LED will flash brightly and briefly when touched to any part of the metal surface. As before, encourage students to connect these observations with the operational models of insulator and conductor. This observation is consistent with charge instantaneously migrating from all parts of the outer metal surface through the LED at once. In pure fact, it occurs over a few nanoseconds.

Students can act out scenarios in which the electric potential is increased or decreased. The goal is to have students increase potential by cramming more charges onto the conducting surface. Removing charges decreases electric potential in this context.

Reduce the area,

Varying charge arrangements,

The stage is set to properly understand electric potential difference in terms of the actual mechanism of surface charge density. Students should be able to articulate the need for a difference in electric potential between two surfaces as the precursor for moving charge. A conductor placed between surfaces allows for charge to move until the surface charge density is equal on both surfaces.

Allow students to role-play moving charge by joining two unequal charge density surfaces with a conductor. Students can freely move across this conducting ‘bridge’ until the surface charge density is equalized. Charging by contact (via sparking) can also be modelled by students leaping across a gap between surfaces — if the electric potential is high enough, i.e. charges crammed very tightly!

By extension, the potential difference between any two points across the two conducting wires in a circuit would also be the same. If bare metal wires are used, this inference can be verified. Careful questioning will help students articulate equal surface charge density on the aluminum plates, the conducting wires and the battery terminals to which they are connected.

A significant question is where the 0.0 V value would lie in this charge depiction? It is exactly midpoint on the (uniform) nichrome resistor of the ‘old-school’ incandescent bulb. This resistor is drawn with a uniformly changing gradient from -3.0 V to +3.0 V, end to end, as shown in the illustration below:

Scaffolding from a simple circuit to series and parallel circuits is achieved by pictorial representations. A two-load series circuit continues the ideal wire scenario and adds a conducting wire between identical loads, as seen below.

Charge distribution across the loads is gradient-driven but along the (ideal) connecting wire it is uniform. If the load resistances are identical, the conducting wire between the loads will be midway in surface charge density, 0.0 V. This conforms to Kirchhoff’s laws regarding the sum of potential differences across the loads equaling the potential difference across the battery. The classic mathematical approach is now solidly anchored by conceptualizing surface charge distribution.

If the loads had unequal resistance, the charge distribution would adjust. If, for example the region between loads obtained a voltage of -1.0 V, it would correspond to potential differences of 4.0 V and 2.0 V, resulting from resistances of 4.0 Ω and 2.0 Ω, as in the diagram below.

Diagram 5 shows three identical resistors in parallel. Charge distribution along the wires is the same as the connected battery terminals, leading to a potential difference of 6.0 V across each load. This indicates an equal current through each resistor and the total current as the sum. If the resistance of each load was

Unequal resistors are equally simple to analyze, beginning with identical potential differences across each load as above. Clearly the current in each loop will vary, inversely to the resistance. The result for total resistance of the circuit RT yields the inverse law for equivalent resistance with multiple resistors in parallel. Being able to visualize the charge distribution augments the mathematical formalism.

Scaling up to combination circuits will likely require application of Kirchhoff’s and Ohm’s laws to establish potential differences before a surface charge distribution diagram could be completed. It would be advisable to have students sketch a surface charge diagram to recognize the combination context is still understandable pictorially. However, the mathematical base provides necessary values for potential difference when a circuit is complex. This helps affirm the value of mathematical formalism with increasingly complex phenomena.

Role-playing provides opportunity for students to discuss, refine and consolidate observations into a shared model of charge distribution, laying solid groundwork for richer analysis. Further, the interactive nature of role-playing engages students who may not flourish in a traditional didactic treatment. The abstract nature of charge is made accessible though inferences anchored in experience with concrete manipulatives.

Teaching through differentiated mathematical, visual and social-interactive methods engages more students thereby establishing a more equitable classroom culture. Diverging from the traditional treatment is risky, so give yourself permission to make mistakes in the process. Have a sense of humour and humility. We are equally students of physics, just further along the continuum of learning. Physics, artfully prepared, should be enjoyed not endured.

- Tatiana V. Goris Purdue University, Common Misunderstandings of Electricity: Analysis of Interview Responses of Electrical Engineering Technology Students; International Journal of Engineering Pedagogy ‒ Volume 6, Issue 1, 2016, p8.
- Streveler, R., Litzinger, T., Miller, R., Steif, P; Learning Conceptual Knowledge in the Engineering Sciences: Overview and Future Research Directions; Journal of Engineering Education, July 2008, p291.
- Carol Dweck; The Remarkable Reach of Growth Mindset; Scientific American, Special Collector’s edition, Winter 2019.
- There are numerous scotch (sticky) tape videos available. One example is: https://www.youtube.com/watch?v=wkBG821cvLU .
- Alzayat, A., Hancock, M., Nacenta, M.; Quantitative Measurement of Virtual vs. Physical Object Embodiment through Kinesthetic Figural After Effects; CHI 2014, One of a CHInd, Toronto, ON, Canada, Session: Multitouch Interaction, p2903-2912.
- Uzma A. S., Shaikh,Alejandra J., Magana, Luis, Neri,David, Escobar-Castillejos, Julieta Noguez and Bedrich Benes; Undergraduate students’ conceptual interpretation and perceptions of haptic-enabled learning experiences; International Journal of Educational Technology in Higher Education. 2017, 14:15
- Balloon materials are usually charged by incidental contact. To neutralize surfaces, a slightly dampened towel can be used to gently stroke the surfaces. Allow to dry thoroughly before testing for neutrality.
- Ontario Ministry of Education, Learning for All, 2013, p 16.
- The author obtained these LED’s from Steve Spangler Science, www.SteveSpanglerScience.com in 2007. The product title was “Static Powered Neon Light.” This type of LED was sold at Radio Shack in the early 1990’s and discontinued. It is not known if Spangler Science is still offering the items for sale.
- Lemon cell batteries to light LED’s. https://www.youtube.com/watch?v=TQHS509_0so
- Boaler, J., Chen, L., Williams, C., Cordero, M.; Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning; Journal of Applied & Computational Mathematics, Vol 5 Issue 5, 2016.
- Goris, T; Common Misunderstandings of Electricity: Analysis of Interview Responses of Electrical Engineering Technology Students; International Journal of Engineering Pedagogy; Vol 6 No 1, 2016