Physics on Your Feet: Berkeley Graduate Exam Questions www.com Physics on Your Feet: Berkeley Graduate Exam Questions or Ninety Minutes of Shame but a PhD for the Rest of Your Life! Second Edition Dmitry Budker University of California, Berkeley, USA and Johannes Gutenberg University, Mainz, Germany Alexander O. Sushkov Boston University, Boston, MA, USA Illustrated by Vasiliki Demas 1 www.com 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Dmitry Budker, Alexander O.
Sushkov, Vasiliki Demas 2015, 2021 The moral rights of the authors have been asserted First Edition published in 2015 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2021934833 ISBN 978–0–19–884236–1 (hbk.0001 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.com To the memory of our teacher and dear friend, Max Zolotorev (1941-2020) www.com Preface to the Second Edition In the few years that passed from the publication of the First Edition of the book, we received a lot of positive feedback and encouragement from our readers and colleagues, which has motivated us to continue keeping an eye out for good questions suitable for oral PhD exams, now also at the Johannes Gutenberg University at Mainz and Boston University, the respective schools where the two of us currently teach (and give examinations).
Some colleagues have offered us such questions, and, as before, we have come up with a number of “exam-style” questions ourselves. The Second Edition extends the book rather significantly, with new problems found towards the ends of the sections and new cartoons skillfully drawn by Dr. Vasiliki Demas added throughout the book. We have also taken the opportunity to correct the (surprisingly few) misprints and minor errors noticed in the First Edition.
We hope the readers continue to find Physics on Your Feet useful and perhaps entertaining! Dmitry Budker Alex Sushkov Mainz and Boston July 2020 www.com Preface to the First Edition How this book came about In May 2010, the Physics Department of the University of California at Berkeley where the two of us, at different times, had been Ph. students, abandoned the Preliminary Oral Examinations, a.a oral prelims, for the first-year graduate students, thus breaking a 60-year-long tradition. In fact, oral examinations were offered at the Berkeley Physics Department much earlier, however, their most recent format and scope more or less settled by 1950, as described by A. Helmholz in his History of the Physics Department.
The Berkeley prelim was a scary experience for those of us on the “receiving end (A.),” and a half-day semi-annual chore for those administering the test (D. did this from Fall of 1995 through Spring of 2010; he “missed” taking the oral prelims as he entered the Berkeley Physics graduate program in 1989 as a continuing student, but has had his share of oral examinations elsewhere). Nevertheless, the two of us strongly feel that this has been extremely useful for the students, providing them, perhaps, the first “real-life” scientific-communication experience, and giving an opportunity to look at the beautiful world of physics in some approximation of completeness. It has also been a truly rewarding experience for the faculty member (D.
One learned a lot from the brilliant students, and from the wise colleagues asking truly interesting and profound questions. Some of the material of this book is drawn from the notes taken by D. at the exams over the years, as well as from the questions collected by the students and passed as an exam-preparation aid “generation to generation.” The origin of the content of the book, therefore, has collective nature, and we are extremely grateful to the members of the Berkeley physics faculty who have generously allowed us to use their ideas. Unfortunately, many of our sources are no longer alive to ask for permission.
We remain in deep gratitude to Profs David Judd, Gil Shapiro, Ronald Ross, and, indirectly, many others. So what’s the point of the book now that the Berkeley orals are no more? We hope this collection will be useful to students (of all ages and everywhere) who wish to refresh and/or test their knowledge of physics, and also to students at the universities that still administer orals. And there are always written prelims, qualifying exams, even at Berkeley (at least, for now). The level of the readers we primarily aim at is upper-division undergraduates and first-year graduate students, although some of these problems will certainly be enjoyed by postdocs and distinguished physics faculty, looking for a fun break from or an unexpected contribution to their research.
We have had a lot of fun writing up the problems for this book, and we would like our readers to share this joy (rather than stress out about the upcoming exam, which is unproductive). We are greatly assisted in this by the eye-pleasing drawings prepared by our skillful illustrator, Dr.com viii Preface to the First Edition m v Other books There are several other collections of problems with the scope and goals partially overlapping with ours. Among these are the following. • Scattering and Structures by (Povh and Rosina, 2005), which is a lovely collection of problems for the German oral Diploma and Ph.
exams with emphasis on quantum phenomena. • A Guide to Physics Problems by Cahn, Mahan, and Nadgorny (Cahn, Mahan, and Nadgorny, 1994), which is a wonderful collection of written examination problem, also supplied with many delightful cartoons (not to mention the most insightful physics). • An impressive multi-volume Problems and Solutions set by a group of Chinese authors (Zhang, Zhou, Zhang, and Lim, 1995; Lim, 1998; Bai, Guo, Lim, 1991; Lim, 2000) compiled by the Physics Coaching class at the University of Science and Technology in China as a guide for preparation to Ph. exams at major American universities.
While this collection appears to be very useful, we find the choice of questions and style of solutions to be substantially different from our own.com How to use this book ix • University of Chicago Graduate Problems in Physics, with Solutions by (Cronin, Greenberg, and Telegdi, 1967) is another great collection, although it generally appears to be more mathematical than this book (and has no cartoons!). • University of California, Berkeley, Physics Problems, with Solutions by (Chen, 1974) is a forty year-old collection of problems based on the Berkeley written Ph. How to use this book We decided to present the solutions right after the problems, instead of separating them into a different part of the book. Nevertheless, as with all respectable problem books, it is recommended that the reader begins by suppressing the temptation to read or peep into the solution right away, and gives the problem an honest “college try” before consulting with the solution (which may be wrong and/or inelegant, anyway).
Some of the material in the solutions clearly goes beyond of what may be expected at an oral examination. We provide these discussions for those readers who may be interested in more in-depth details about the subject and mark the corresponding passages that can be omitted without sacrificing the quality of exam preparation by placing them in the “aside” environment as this paragraph. Have fun and good luck! Dmitry Budker Alexander O. Sushkov Berkeley and Harvard March 2014 www.com Acknowledgements The original title of this book with which we “lived” for a long time was Ninety Minutes of Shame (but a PhD in Physics for the rest of your life), however, our OUP Editor, Sonke Adlung warned us that this title puts book in serious danger of landing in a wrong section of a bookstore.
We are deeply grateful to Sonke for his patient help and guidance over the years it took to complete this project. This book would not have been possible without our mentors, colleagues, and students whose ideas inspired many of the problems and solutions found in this book. Their suggestions, guidance, and readings of countless drafts were invaluable, and we sincerely appreciate their contributions. In the semester preceding the completion of the book (Fall 2013), D.
taught an undergraduate senior elective course at Berkeley called “Physics for Future Physicist” largely based on the problems in the book. The feedback from the students (several of whom actually non-physicists) was enormously helpful. Some people we would like to acknowledge specifically are Derek Jackson Kimball, Marcis Auzinsh, Byung-Kyu Park, Sean Carroll, Eugene D. Commins, Mikhail Kozlov, Oleg Sushkov, Victor Acosta, Angom Dilip Kumar Singh, Vladimir G.
Muller, Nathan Leefer, Ron Walsworth, Max Zolo- torev, Steve Lamoreaux, Gregory Falkovich, Pauli Kehayias, Konstantin Tsigutkin, Brian Patton, Michael Solarz, Ron Folman, Szymon Pustelny, Ori Ganor, Michael Ho- hensee, Mikhail Lukin, Ran Fischer, D. Chris Hovde, Yehuda B. Band, Joel Fajans, Peter Milonni, Sifan Wang, Sean Lourette, Maria Simanovskaia, Simon Rochester, and Tamara Sushkova. Damon English helped to set this project in motion and provided invaluable input at its early stages.
In conjunction with the Second Edition, we would like to acknowledge, in addi- tion to the individuals listed previousley, Arne Wickenbrock, Valerii Zapasskii, Masha Baryakhtar, Lykourgos Bougas, and Diana Saville. The authors acknowledge the support of their research, that motivated many of the problems in this book.com Contents 1 Mechanics, Heat, and General Physics 1 1.5 Mechanical oscillator as a force sensor 11 1.6 Hot-dog physics 15 1.10 Lightbulb and coal 25 1.11 Comfortable walking speed 27 1.12 Rotating dumbbell 29 2 Fluids 32 2.2 Bubble and pressure 37 2.4 Surprises in melting and solidification 43 2.5 Shallow-water and deep-water gravity waves 47 2.7 Boat speed limit (hull speed) 53 2.8 Floating in circles 55 2.10 Temperature lapse in the atmosphere 59 2.11 Angler’s dilemma 63 3 Gravitation, Astrophysics, and Cosmology 66 3.1 Olber’s paradox: why is the sky dark? 67 3.2 Gravitational shift of clock rates 69 3.4 Planck mass and length scale 75 3.5 Rotation of stars around the center of a galaxy 77 3.6 Ultralight dark matter 79 3.7 Detecting gravitational waves 83 3.8 Dark matter trapped in the Earth 87 4 Electromagnetism 90 4.1 Currents and magnetic fields 91 4.2 Electromagnet design 95 www.com xii Contents 4.3 Field in a shield (with a coil) 97 4.5 Energy in a wire 105 4.6 Earth’s magnetic field angle 109 4.7 Refrigerator-magnet science 111 4.8 Spherical-cell magnetometer 115 4.9 Magnetic force on a superconducting magnet 117 4.10 Circuit view of atoms and space 121 4.11 Magnetic monopole 125 5 Optics 128 5.1 Rotating liquid mirror 129 5.5 Diffraction on an edge 141 5.6 Black-body radiation 143 5. thermal light source 145 5.8 Correlation functions for light and Bose condensates 149 5.9 Pulsed laser repetition rate 153 5.11 Rotating linear polarization 159 6 Quantum, Atomic, and Molecular Physics 162 6.1 Magnetic decoupling of spins 163 6.3 Bound states in a potential well 169 6.4 Hypothetical anomalous hydrogen 177 6.5 Time-reversal in quantum mechanics 181 6.9 Van der Waals interaction 193 6.