Improving efficiency ininstruction: Gauss’s law
Marshall J. Styczinski
Physics Education GroupUniversity of Washington
July 18th, 2016AAPT Summer Meeting
Physics
Education
Group
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Tutorials in introductory physics
University of WashingtonIntroductory physics:
3 hrs/week lecture1 hr/week tutorial2 hrs/week lab
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Tutorials in introductory physics
University of WashingtonIntroductory physics
1 hr/week tutorial
Each tutorial addressesknown student difficulties
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Physics
Education
Group
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Physics
Education
Group
10 or fewer weekly tutorials
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Topics to combine
Forces & Newton’s second and third lawsLenz’s law & Faraday’s lawElectric field and flux & ChargeElectric field and flux & Gauss’s law
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Topics to combine
Forces & Newton’s second and third lawsLenz’s law & Faraday’s lawElectric field and flux & ChargeElectric field and flux & Gauss’s law
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R1
R2
Q
Non-conductor
Total charge Q spreadthroughout volumeThick spherical shell, insulatorQuestion: Find | ~E| in the shell.
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R1
R2
Q
Non-conductor
Total charge Q spreadthroughout volumeThick spherical shell, insulatorQuestion: Find | ~E| in the shell.
Required concepts:Distributed chargesCharge densitySurface area vs. volume
Electric fieldElectric flux
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R1
R2
Q
Non-conductor
Total charge Q spreadthroughout volumeThick spherical shell, insulatorQuestion: Find | ~E| in the shell.
N = 308
15% obtained a correct expression.< 5% explained how they obtained correct
expressions.
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The literature
The Gauss’s law tutorial improves conceptualunderstanding of Gauss’s law.1
1Kanim, S. (1999)
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The literature
The Gauss’s law tutorial improves conceptualunderstanding of Gauss’s law.1
Helping students learn about symmetry withflux and applicability of Gauss’s law improvesunderstanding and problem solving ability.2
1Kanim, S. (1999)2Singh, C. (2006)
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Gauss’s law tutorial coverage
Flux practice+Q
o
Finding basic Qenc
–Qo
+Qo
–Qo
+Qo
Examplecalculation
+σo
Find ER
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Existing tutorials
Week 1
Week 2
Week 3
Charge
Gauss’s law
Electric field
and flux
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Existing tutorials New tutorials
Week 1
Week 2
Week 3
Charge
Gauss’s law
Charge and
Electric field
and flux
electric field
Flux and
Gauss’s law
Marshall Styczinski (U Washington) AAPT Summer Meeting 9 / 16
Existing tutorials New tutorials
Week 1
Week 2
Week 3
Charge
Gauss’s law
Charge and
Electric field
and flux
electric field
Flux and
Gauss’s law
New content!
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Existing tutorials New tutorials
Week 1
Week 2
Week 3
Charge
Gauss’s law
Charge and
Electric field
and flux
electric field
Flux and
Gauss’s law
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Electric field and
flux (existing)
Flux and
Gauss’s law (new)
Gauss’s law
(existing)
Area vector
Relate electric force
to field
Explore the
field of a vertical
charged rod
Test charge
independence
Finding
sign of flux
Electric
field lines
Finding flux in a
non-uniform field
Verify Gauss’s
law consistency
Finding
basic Qenc
Applying
Gauss’s law
Superposition
in Gauss’s law
Area vector
Finding flux signs
and magnitudes
Finding flux in a
non-uniform field
Relate basic Qenc
to independently
found Φnet
Confront difficulties
about non-closed surfaces
(BASED ON SINGH 2006)
Symmetry considerations
(BASED ON SINGH 2006) (To HW)
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Physics
Education
Group
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Difficult for students:1
Flux throughportion of aGaussian surfaceSuperposition and“blocking” of fieldsTutorial helps withthese
1Kanim, S. (1999)
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Difficult for students:1
Flux throughportion of aGaussian surfaceSuperposition and“blocking” of fieldsTutorial helps withthese
Large sheet,
+σo
+q
Added
ΦL
Gaussian
surface
Question: Does ΦL increase,
decrease, or remain the same?1Kanim, S. (1999)
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Impact of changes
10%
30%
50%
Correct
reasoning
Ignored
point charge
Applied Gauss’s
law to end cap
Incorrect
reasoning
Lined: original, N = 238
Solid: modified, N = 302
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With the new Flux and Gauss’s law tutorial:Students were about equally-well preparedReduced class time:We did more the same with less!Made room to cover more topics
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Next steps
Further validation of flux and Gauss’s lawOptimize time spent/condense more tutorials:
Forces & Newton’s second and third lawsLenz’s law & Faraday’s law
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Next steps
+
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Thank you for coming!Acknowledgments:
Grant No. DUE-1022449
Physics
Education
Group
Aziz Khan
Other UWPEGmembers:
Lillian McDermottPeter ShafferPaula HeronDonna MessinaRyan HazeltonPaul EmighAlexis OlshoBert XueTong WanSheh Lit ChangLisa Goodhew
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Exam questionsOlder conceptual question: N = 238
ΦR
Cube
Gaussian
surface d
d
Hollow sphere,
non-conducting
Sphere
Changes
sides
uniform
+ charge
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Exam questionsNewer conceptual question: N = 302
+σo
−qo
Case 1
Gaussian
surface
+4qo
enclosed
+σo
Translated
closer
−qo
ΦL
Case 2
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Exam responsesInitial calculation question (E in thick chargedshell): N = 308
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Exam responsesCorrect explanation
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Exam responses
“Ignored point charge” explanation
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Exam responses
“Applied Gauss’s law” explanation
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