Improving efficiency in instruction: Gauss s law
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1 Improving efficiency in instruction: Gauss s law Marshall J. Styczinski Physics Education Group Physics Education Group University of Washington July 18th, 2016 AAPT Summer Meeting Marshall Styczinski (U Washington) AAPT Summer Meeting 1 / 16
2 Marshall Styczinski (U Washington) AAPT Summer Meeting 2 / 16
3 Tutorials in introductory physics University of Washington Introductory physics: 3 hrs/week lecture 1 hr/week tutorial 2 hrs/week lab Marshall Styczinski (U Washington) AAPT Summer Meeting 3 / 16
4 Tutorials in introductory physics University of Washington Introductory physics 1 hr/week tutorial Each tutorial addresses known student difficulties Marshall Styczinski (U Washington) AAPT Summer Meeting 3 / 16
5 Physics Education Group Marshall Styczinski (U Washington) AAPT Summer Meeting 4 / 16
6 Physics Education Group 10 or fewer weekly tutorials Marshall Styczinski (U Washington) AAPT Summer Meeting 4 / 16
7 Topics to combine Forces & Newton s second and third laws Lenz s law & Faraday s law Electric field and flux & Charge Electric field and flux & Gauss s law Marshall Styczinski (U Washington) AAPT Summer Meeting 5 / 16
8 Topics to combine Forces & Newton s second and third laws Lenz s law & Faraday s law Electric field and flux & Charge Electric field and flux & Gauss s law Marshall Styczinski (U Washington) AAPT Summer Meeting 5 / 16
9 Non-conductor Q R 1 R 2 Total charge Q spread throughout volume Thick spherical shell, insulator Question: Find E in the shell. Marshall Styczinski (U Washington) AAPT Summer Meeting 6 / 16
10 Non-conductor Q R 1 R 2 Total charge Q spread throughout volume Thick spherical shell, insulator Question: Find E in the shell. Required concepts: Distributed charges Charge density Surface area vs. volume Electric field Electric flux Marshall Styczinski (U Washington) AAPT Summer Meeting 6 / 16
11 Non-conductor Q R 1 R 2 Total charge Q spread throughout volume Thick spherical shell, insulator Question: Find E in the shell. N = % obtained a correct expression. < 5% explained how they obtained correct expressions. Marshall Styczinski (U Washington) AAPT Summer Meeting 6 / 16
12 The literature The Gauss s law tutorial improves conceptual understanding of Gauss s law. 1 1 Kanim, S. (1999) Marshall Styczinski (U Washington) AAPT Summer Meeting 7 / 16
13 The literature The Gauss s law tutorial improves conceptual understanding of Gauss s law. 1 Helping students learn about symmetry with flux and applicability of Gauss s law improves understanding and problem solving ability. 2 1 Kanim, S. (1999) 2 Singh, C. (2006) Marshall Styczinski (U Washington) AAPT Summer Meeting 7 / 16
14 Gauss s law tutorial coverage Flux practice +Q o Finding basic Q enc Example calculation +σ o +Q o Q o Q o +Q o Find E R Marshall Styczinski (U Washington) AAPT Summer Meeting 8 / 16
15 Existing tutorials Week 1 Charge Week 2 Electric field and flux Week 3 Gauss s law Marshall Styczinski (U Washington) AAPT Summer Meeting 9 / 16
16 Week 1 Existing tutorials Charge New tutorials Charge and electric field Week 2 Electric field and flux Flux and Gauss s law Week 3 Gauss s law Marshall Styczinski (U Washington) AAPT Summer Meeting 9 / 16
17 Week 1 Existing tutorials Charge New tutorials Charge and electric field Week 2 Electric field and flux Flux and Gauss s law Week 3 Gauss s law New content! Marshall Styczinski (U Washington) AAPT Summer Meeting 9 / 16
18 Week 1 Existing tutorials Charge New tutorials Charge and electric field Week 2 Electric field and flux Flux and Gauss s law Week 3 Gauss s law Marshall Styczinski (U Washington) AAPT Summer Meeting 9 / 16
19 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 Area vector Finding flux signs and magnitudes Finding flux in a non-uniform field Finding flux in a non-uniform field Verify Gauss s law consistency Finding basic Q enc Test charge independence Relate basic Q enc to independently found Φ net Applying Gauss s law Finding sign of flux Electric field lines Confront difficulties about non-closed surfaces (BASED ON SINGH 2006) Symmetry considerations (BASED ON SINGH 2006) (To HW) Superposition in Gauss s law Marshall Styczinski (U Washington) AAPT Summer Meeting 10 / 16
20 Physics Education Group Marshall Styczinski (U Washington) AAPT Summer Meeting 11 / 16
21 Difficult for students: 1 Flux through portion of a Gaussian surface Superposition and blocking of fields Tutorial helps with these 1 Kanim, S. (1999) Marshall Styczinski (U Washington) AAPT Summer Meeting 12 / 16
22 Difficult for students: 1 Flux through portion of a Gaussian surface Superposition and blocking of fields Tutorial helps with these Gaussian surface Φ L Large sheet, +σ o Added +q Question: Does Φ L increase, decrease, or remain the same? 1 Kanim, S. (1999) Marshall Styczinski (U Washington) AAPT Summer Meeting 12 / 16
23 Impact of changes 50% 30% Lined: original, N = 238 Solid: modified, N = % Ignored point charge Applied Gauss s law to end cap Correct reasoning Incorrect reasoning Marshall Styczinski (U Washington) AAPT Summer Meeting 13 / 16
24 With the new Flux and Gauss s law tutorial: Students were about equally-well prepared Reduced class time: We did more the same with less! Made room to cover more topics Marshall Styczinski (U Washington) AAPT Summer Meeting 14 / 16
25 Next steps Further validation of flux and Gauss s law Optimize time spent/condense more tutorials: Forces & Newton s second and third laws Lenz s law & Faraday s law Marshall Styczinski (U Washington) AAPT Summer Meeting 15 / 16
26 Next steps + Marshall Styczinski (U Washington) AAPT Summer Meeting 15 / 16
27 Thank you for coming! Acknowledgments: Grant No. DUE Physics Education Group Aziz Khan Other UWPEG members: Lillian McDermott Peter Shaffer Paula Heron Donna Messina Ryan Hazelton Paul Emigh Alexis Olsho Bert Xue Tong Wan Sheh Lit Chang Lisa Goodhew Marshall Styczinski (U Washington) AAPT Summer Meeting 16 / 16
28 Exam questions Older conceptual question: N = 238 Cube Gaussian surface Hollow sphere, non-conducting d uniform + charge Sphere Changes sides d Φ R Marshall Styczinski (U Washington) AAPT Summer Meeting 17 / 16
29 Exam questions Newer conceptual question: N = 302 Case 1 Case 2 Gaussian surface +σ o Translated closer +σ o q o q o Φ L +4q o enclosed Marshall Styczinski (U Washington) AAPT Summer Meeting 18 / 16
30 Exam responses Initial calculation question (E in thick charged shell): N = 308 Marshall Styczinski (U Washington) AAPT Summer Meeting 19 / 16
31 Exam responses Correct explanation Marshall Styczinski (U Washington) AAPT Summer Meeting 20 / 16
32 Exam responses Ignored point charge explanation Marshall Styczinski (U Washington) AAPT Summer Meeting 21 / 16
33 Exam responses Applied Gauss s law explanation Marshall Styczinski (U Washington) AAPT Summer Meeting 22 / 16
c Copyright 2017 Alexis Rebecca Werner Olsho
c Copyright 2017 Alexis Rebecca Werner Olsho An Investigation of Introductory Student Understanding of Special Relativity in the Context of the Relativity of Simultaneity Alexis Rebecca Werner Olsho A
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