Physics 8B Stahler Fall 2020 Final Exam questions PDF

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Physics 8B Stahler Fall 2020 Final Exam questions...

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PHYSICS 8B – Fall 2020 - S. Stahler & C. Bordel Lecture 2, Final Exam Friday, December 18th, 8:00 – 11:00 AM Details: •

Time: You will have 3 hours to complete the exam, and 20 minutes to scan and upload it. o The exam is designed to take 3 hours.

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Submission: The exam will be submitted via Gradescope. o We ask that you start a new page for each problem. o You are not required to write on a printed copy of the exam.

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Allowed: This midterm is open book and open notes and calculators are allowed. o You are not allowed to communicate with any other students or discuss the content of the exam with anyone besides the Physics 8B teaching staff. o The use of homework help sites is strictly forbidden and will result in disciplinary action.

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Grading: Partial credit will be awarded on this exam. o You must show all of your work/clearly explain your reasoning in order to receive credit for answers. o Partial credit will be awarded on solutions to this exam. o Answers to all non-numerical questions must be expressed in terms of fundamental constants of nature and the variables provided in the question.

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Questions: All questions during the exam should be asked as private messages via Zoom or as emails to James Parkes ([email protected]).

Academic Integrity: It is expected that during this examination, as with any examination that students adhere to the usual standards of academic integrity at the University of California at Berkeley as outlined on by the Center for Teaching and Learning. Therefore, by submitting the exam to Gradescope, you are affirming the following statement:

“I swear on my honor that I have neither given nor received aid on this exam from persons, homework help sites, etc. In addition, I abided by all of the examination policies as outlined above.”

Problem 1 (25 points) Two metal balls are glued to the ends of a stick of length L. The stick is made of insulating material. The balls have charges +Q and −Q.

(a) With what force F does the stick push upward on the top ball? You may ignore gravity throughout this problem.

(b) Consider a point A, located a distance L above the center of the stick. Find the magnitude and direction of EA , the electric field at this point.

√ (c) Next consider a point B , located a perpendicular distance 3 L/ 2 from the center of the stick. Find both the magnitude and direction of EB , the electric field at this point.

(d) Finally, consider an imaginary ellipsoidal surface, whose center coincides with that of the stick, and which passes through both points A and B. What is ΦE , the electric flux through this surface? Tell us both the magnitude and algebraic sign of this quantity.

Problem 2 (25 points) Consider the long, kinked wire in the figure below; this wire carries a steady current i. In the figure, parts of the wire extending to spatial infinity are shown dashed. The two finite segments, of length d1 and d2 , form a right angle and intersect at point O. Your task is to determine B0 , the magnetic field at this point.

(a) Using the Biot-Savart law, find B1 and B2 , the magnitudes of the fields from d1 and d2 , respectively.

(b) Find Bh , the magnitude and direction of the field from the horizontal, semi-infinite portion. (Hint: What would the field be if this portion of the wire were infinite in both directions?)

(c) In the same manner, find Bv , the field from the vertical, semi-infinite portion.

(d) Finally, calculate both the magnitude and direction of B0 .

Problem 3 (25 points) You are asked by a dentist to design a small mirror. The request is that the image of a tooth should be upright and twice as large as the tooth itself when the mirror is placed at distance d from the tooth. a) Determine the nature (convex or concave) and radius of curvature of such a mirror.

b) Do the ray tracing, with a fully consistent scale, to show where the image of the tooth is formed through the mirror.

The mirror is designed to be held at distance D=2d from the eye for a normal eye. However, the dentist is actually farsighted and cannot clearly see objects closer than L, where L=5d. You may assume that the dentist's eye, the tooth and the mirror are all along the same line. c) Determine whether or not the dentist needs to wear his corrective lenses to be able to clearly see the image of the tooth formed by the mirror, when held at the recommended distance.

d) Determine the required focusing power of the dentist's corrective lenses that allows him to see the image of the tooth clearly. You may assume that the corrective lenses are worn at a negligible distance from the eye lens. Hint: the image of the tooth through the mirror needs to be transformed by the corrective lens so that its image will be located at the closest point of clear vision for the defective eye.

Problem 4 (25 points) We consider a double-slit interferometer where the narrow slits of width a, separated by a spacing d, are equidistant from the source which emits a monochromatic light of wavelength λ. The interference pattern is observed on a screen that is placed at distance L from the slits. The slits have been chosen so that d/a=3, and you may assume that λ...