(10/06) Lecture Learning Assistant Program Overview and Parallel Plate Capacitance

Learning Assistant Program Structure and Objectives

• Definition of Learning Assistants (LAs): Undergraduate students who have successfully completed a STEM course or its equivalent and return to assist current students during active in-class problem-solving sessions.

• Core Responsibilities and Weekly Commitments:

  • Facilitating challenging in-class activities in collaboration with primary course instructors.

  • Attending mandatory weekly faculty prep meetings (e.g., meeting every Friday with Dr. Sivran) to pre-solve and review upcoming course curriculum.

  • Enrolling in a required pedagogy course during their first semester as an LA to study educational theory and the science of teaching.

  • Providing out-of-classroom peer tutoring at academic support facilities such as the Physics Study Center.

  • Partnering with faculty in STEM Communities project teams to redevelop and optimize course curricula (e.g., redesigning course modules during summer sessions).

Quantitative Impact of Learning Assistants on Student Performance

• Definition of DFW Rate: The combined percentage of enrolled students who receive a grade of D, F, or who withdraw (W) from a course, requiring them to repeat the class.

• Historical Course Performance Data at Texas State University:

  • Prior to the integration of the LA program, DFW rates in introductory physics (mechanics) exceeded $50\%$, forcing over half of all enrolled students to retake the course.

  • Following LA implementation, DFW rates exhibited a significant and continuous decline, evaluated through Fall 2017 and beyond across both Mechanics and Electricity & Magnetism (E&M / ENAP) course sequences.

  • The reduction in DFW rates corresponded directly with an upward shift in student grade distributions, yielding a higher proportion of A and B final grades.

• Advanced Academic Outcomes (University of Colorado at Boulder Assessment Data):

  • Longitudinal performance tracking in senior upper-level Electricity and Magnetism courses evaluated students based on their introductory E&M course background:

  • Students from traditional lecture-based introductory courses achieved an average performance score of $55\%$ in upper-level E&M.

  • Students from interactive, LA-supported introductory courses achieved an average performance score of $75\%$ in upper-level E&M.

  • Students who served as LAs during their introductory E&M course achieved an average performance score of $90\%$ in upper-level E&M.

LA Program Employment, Compensation, and Application Details

• Eligible Disciplines: Undergraduate STEM courses across Biology, Chemistry, and Physics (including engineering/physics major sequences and life science major sequences).

• Academic Qualification Threshold: Completion of the target course or an equivalent course. Earned grades of B or high C demonstrate sufficient foundational understanding to be a competitive candidate.

• Financial Compensation and Hour Allocations:

  • Base pay rate: $14.00 per hour (with active in-class LAs, such as Aurelia, compensated at $15.00 per hour).

  • Time commitment: 5 to 10 hours per week.

  • Paid hours cover in-class instructional support, the 2-hour mandatory Friday faculty prep session, and assigned tutoring hours at the Physics Study Center.

  • Unpaid Pedagogy Course: The first-semester pedagogy course is taken for academic credit (eligible for upper-level credit in Honors, Biology, Chemistry, or Physics) rather than hourly wages.

• Application and Selection Timeline:

  • Application deadline: Sunday, October 11th at midnight.

  • Selection workflow: Online application submission, candidate interviews, notification of acceptances prior to the conclusion of the fall semester, participation in a mandatory 2-hour pre-semester orientation workshop, and official placement starting on Day 1 of the Spring 2027 semester.

Group Dynamics and Pedagogical Rationale for Table Rotation

• Classroom Organization: Students are arranged into designated small groups across numbered laboratory tables (Tables 1 through 8).

• Pedagogical Research on Group Composition:

  • Educational research demonstrates that remaining in static social groups or isolated single-gender pairings can lead to counterproductive social chemistry, slowing learning velocity and masking individual group dysfunction.

  • Periodic group rotation trains students to adapt to dynamic team structures, reflecting professional engineering and scientific working environments where team assignments are externally determined.

Fundamental Principles of Capacitance and Parallel Plate Geometry

• Definition of Capacitance ($C$): The physical quantity measuring the amount of electric charge ($Q$) a conductor or device can store per unit of electric potential difference ($V$):

  $C = \frac{Q}{V}$

• SI Units: Measured in Coulombs per Volt ($\text{C/V}$), defined as Farads ($\text{F}$).

• Parallel Plate Capacitor Structure:

  • Consists of two parallel conducting plates separated by a distance $d$, each possessing plate area $A$.

  • Charges are equal in magnitude and opposite in sign: positive charge ($+Q$) resides on one plate and negative charge ($-Q$) on the opposing plate.

  • Surface charge density ($\sigma$) on each plate is defined as:

    $\sigma = \frac{Q}{A}$

• Finite vs. Infinite Plate Approximations:

  • Theoretical physics models assume infinite parallel plates to create a perfectly uniform electric field with zero edge fringing.

  • Practical engineering and real-world project applications utilize finite plate dimensions, requiring accounting for field distortion along plate boundaries.

Work, Electric Potential Difference, and Field Interactions

• Work Done on Electric Charges:

  $W = \mathbf{F} \cdot \mathbf{d} = F \, d \, \cos(\theta)$

• Electric Potential Difference Relation:

  $\Delta V = -\frac{W}{q}$

• Motion Relative to Electric Field Lines:

  • When moving a positive charge along the electric field direction ($\theta = 0^\circ$), $\cos(0^\circ) = 1$, electric force does positive work, reducing electric potential energy.

  • When displacing a charge against the direction of the electric field ($\theta = 180^\circ$), $\cos(180^\circ) = -1$, external work is performed against the field, increasing electric potential difference:

    $\Delta V = E \, d$

Behavior of Capacitors Under Differing Physical Boundary Conditions

• Isolated (Disconnected) Capacitor System:

  • Boundary condition: Total stored charge remains constant ($Q = \text{constant}$) because charges are insulated and cannot flow off the plates.

  • Constant parameters: Surface charge density ($\sigma = \text{constant}$) and electric field strength ($E = \frac{\sigma}{\varepsilon_0} = \text{constant}$).

  • Effect of increasing plate separation distance ($d$):

  • Potential difference increases linearly: $\Delta V = E \, d$

  • Capacitance decreases according to:

      $C = \frac{\varepsilon_0 A}{d}$

• Battery-Connected (Constant Voltage) Capacitor System:

  • Boundary condition: Potential difference remains fixed at the battery voltage ($V = V_0$).

  • Effect of increasing plate separation distance from initial $d$ to larger distance $D$:

  • Electric field decreases according to:

      $E = \frac{V_0}{D}$

- Surface charge density ($\sigma$) and stored charge ($Q$) decrease proportionally by the factor $\frac{d}{D}$.
- Capacitance decreases according to:

      $C = \frac{\varepsilon_0 A}{D}$

Student Q&A and Operational Class Discussions

• Question: When does an applicant officially start their duties after applying and being accepted into the LA program?

• Answer: Official duties begin on Day 1 of the Spring 2027 semester, following an application review, interview process, end-of-semester acceptance notification, and a mandatory 2-hour orientation workshop conducted prior to the start of classes.

• Question: How does a battery connection affect potential difference when capacitor plates are moved further apart?

• Answer: The battery holds the potential difference strictly constant at $V_0$. As separation distance increases, the electric field strength decreases ($E = \frac{V_0}{d}$), causing electric charge to flow off the plates and reducing charge density $\sigma$.

• Course Administrative Details:

  • Quizzes are administered via Canvas under designated module images (e.g., Image 3, page 111 top-right diagram).

  • Lab report due dates are updated on Canvas following institutional schedule shifts and academic breaks.