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The instructions specify how to label parts and sub-parts, use black or dark blue ink, and show work with units for numerical answers. Question 1 (Version J) addresses electric field and potential for a coaxial cylindrical capacitor using Gauss’s law, sketching E versus r, and then dielectric insertion to derive capacitance. Question 2 (Version J) focuses on a rotating conducting loop in a uniform magnetic field, requiring induced emf values and bar-chart construction over specified times.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/ap-physics-c-electricity-and-magnetism-free-response-questions/458382/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/ap-physics-c-electricity-and-magnetism-free-response-questions/458382.png","ImageObject",300,407,{"name":92,"@type":93},"Theodore","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-21","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the timing and number of questions in Section II?","Question",{"text":112,"@type":113},"Section II lasts 1 hour and 40 minutes and contains 4 questions.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What are the rules for writing answers and scoring expectations?",{"text":117,"@type":113},"Label parts and sub-parts as needed, write in black or dark blue ink, include appropriate units for numerical answers, and show work so credit can be awarded for applying the correct physics principles.",{"name":119,"@type":110,"acceptedAnswer":120},"What topics are covered in Question 1 and Question 2?",{"text":121,"@type":113},"Question 1 derives electric field and potential for a coaxial cylindrical capacitor, sketches E versus r, and then finds capacitance after inserting a dielectric. 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College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered trademarks [of College Board. Visit College Board on the web: collegeboard.org](of College Board. Visit College Board on the web: collegeboard.org).  \nAP Central is the official online home for [the AP Program: apcentral.collegeboard.org](the AP Program: apcentral.collegeboard.org).  \nPHYSICS C: ELECTRICITY AND MAGNETISM  \nSECTION II  \nTIME – 1 HOUR AND 40 MINUTES  \nDirections:  \nSection II has 4 questions and lasts 1 hour and 40 minutes.  \nYou may use the available paper for scratch work and planning, but you must write your answers in the free-response booklet. Label parts (e.g., A, B, C) and sub-parts (e.g., i, ii, iii) as needed. Use a pencil or a pen with black or dark blue ink to write your responses.  \nA calculator is allowed in this section, as well as a ruler and straightedge. You may use a handheld four-function, scientific, or graphing calculator, or the calculator available in this application. Reference information, including lists of equations, can also be accessed in this application and is available throughout the exam.  \nAll final numerical answers should include appropriate units when applicable. Credit for your work depends on demonstrating that you know which physical principles to apply in a particular situation. Credit will be awarded only for work that is clearly designated as the solution to a specific part of a question. Credit also depends on the quality of your solutions and explanations. Therefore, you should show your work for each part in the space provided for that part. If you need more space, be sure to clearly indicate where you continue your work. When constructing a graph or diagram, use only one color of ink or pencil.  \nYou may pace yourself as you answer the questions in this section, or you may use these optional timing recommendations:  \nIt is suggested that you spend about 25 minutes each on Questions 1 and 3, about 30 minutes on Question 2, and about 20 minutes on Question 4.  \nYou can go back and forth between questions in this section until time expires. The clock will turn red when 5 minutes remain—the proctor will not give you any time updates or warnings.  \nNote: This exam was originally administered digitally. It is presented here in a format optimized for teacher and student use in the classroom.  \nDuring the AP Exam administration, students have access to reference information. To see the reference information for this course, please visit AP Central:  \n[https://apcentral.collegeboard.org/courses/ap-physics-c-electricity-and-magnetism/exam](https://apcentral.collegeboard.org/courses/ap-physics-c-electricity-and-magnetism/exam)  \n© 2025 College Board.  \n[Visit College Board on the web:](Visit College Board on the web: collegeboard.org 2)[ collegeboard.org](Visit College Board on the web: collegeboard.org 2)[ 2](Visit College Board on the web: collegeboard.org 2)  \nQuestion 1: Version J  \n1. An isolated, air-filled, charged capacitor consists of two conducting, coaxial, cylindrical shells that each have length L. The inner shell has radius R1 and the outer shell has radius R2 , as shown in Figure 1, where R1 \u003C R2 % L. The surface charge densities (amounts of charge per unit area) of the inner and outer shells are + v1 and-v2 , respectively. The absolute values of the total charges on the shells are equal.  \nA.  \ni. Using Gauss’s law, derive an expression for the magnitude E of the electric field asa function of the radial distance r from the center of the capacitor for the region R1 \u003C r \u003C R2. Express your answer in terms of R1 , v1 , r, and physical constants, as appropriate.  \nii. Derive an expression for the absolute value TV of the potential difference between the outer and inner shells in terms of R1 , R2 , v1 , and physical constants, as appropriate. Begin your derivation by writing a fundament","cbCaigHeSjVRRJq0","https://ap.wps.com/l/cbCaigHeSjVRRJq0","pdf",457935,"English","# Section II Instructions\n## Timing and question structure\n## Answering, units, and showing work\n# Question 1 (Version J)\n## Electric field and potential of a coaxial capacitor\n## E vs r graph\n## Dielectric insertion and capacitance\n# Question 2 (Version J)\n## Rotating conducting loop in a uniform magnetic field\n## Induced emf and bar chart values","[{\"question\":\"What are the timing and number of questions in Section II?\",\"answer\":\"Section II lasts 1 hour and 40 minutes and contains 4 questions.\"},{\"question\":\"What are the rules for writing answers and scoring expectations?\",\"answer\":\"Label parts and sub-parts as needed, write in black or dark blue ink, include appropriate units for numerical answers, and show work so credit can be awarded for applying the correct physics principles.\"},{\"question\":\"What topics are covered in Question 1 and Question 2?\",\"answer\":\"Question 1 derives electric field and potential for a coaxial cylindrical capacitor, sketches E versus r, and then finds capacitance after inserting a dielectric. Question 2 analyzes the induced emf in a rotating conducting loop in a uniform magnetic field and requires bar-chart values at specified times.\"}]","AP® Physics C: Electricity and Magnetism - Free-Response Questions | PDF",1790752780,25]