Physics midterm question: scuffing your shoes on a rug and jumping up

Physics 205B Midterm 2, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 17.22, Problems 17.55, 17.56

A voltmeter is used to measure the potential difference between a person's shoes and a rug[*]:
Scuff [your shoes] on the rug, and watch the voltage-reading on the meter [connected to the shoes and the rug] as it climbs up to several thousand volts... To make the voltage go up, leap into the air.
Assume that the shoes and the rug act as a parallel-plate capacitor, and that the amount of charge stored remains constant as the person leaps up in the air. Discuss why the voltmeter reading increases when the person leaps up into the air. Explain your reasoning by using the properties of capacitors, charge, and electric potential.

[*] William J. Beaty, "'Static Electricity' means 'High Voltage'--Measuring your Body-Voltage," amasci.com/emotor/voltmeas.html.

Solution and grading rubric:
  • p:
    Correct. Discusses/demonstrates:
    1. that an increase in distance between capacitor plates (shoe and rug) decreases their capacitance C = A/(4π∙kd); and
    2. a decrease in capacitance, while charge remains the same results in an increase in voltage difference ΔV = Q/C.
    May instead argue from work argument that the electric potential energy of two oppositely (but equal amounts) of charge will increase when they are separated from each other, resulting in an increase in ΔV.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying applying properties of capacitors, charge, and electric potential.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of applying properties of capacitors, charge, and electric potential.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 30882, 30883
Exam code: midterm02m3tR
p: 35 students
r: 0 students
t: 8 students
v: 3 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 8984):

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