, Contents
Introduction 7
Questions and Problems 10
1. Fundamentals of Mechanics to
2. Molecular Physics and Thermodynamics 25
3. Electrostatics 42
4. Direct Current 54
5. Electromagnetism 67
6. Oscillatory Motion and Waves 80
7. Alternating Current 92
8. Optics 95
9. Atomic and Nuclear Physics t09
Answers and Solutions 121
1. Fundamentals of Mechanics 121
2. Molecular Physics and Thermodynamics t55
3. Electrostatics 188
4. Direct Current 213
5. Electromagnetism 233
6. Oscillatory Motion and Waves 254
7. Alternating Current 275
8. Optics 286
9. Atomic and Nuclear Physics 316
Postface 335
, A drawing is the source and soul
of every image and the root of every
science."
Michelangelo
Introduction
The student put down his record book and picked up an
examination card. Upon reading it, he gasped: "My God!
What will I do?" Judging by his face, one would think
be held at the very least a poisonous snake. The assign-
ment on the card read: "The velocity distribution of mol-
ecules; the Maxwellian curve." The student was not re-
quired to derive the formula or even write out the formu-
la. All he had to do was to draw the curve and explain its
physical meaning. Another student, in drawing the van
der Waals isotherm depicted something resembling a ca-
mel with two humps; moreover, the curve passed through
the origin. Still another student, while explaining the
idea behind the Stern experiment, made the outer cylin-
der rotate while the inner cylinder remained fixed. Fi-
nally, to the question of how the temperature of a gas
changes under adiabatic expansion a student gave the
following "reasonable" answer: since objects expand when
heated, and the gas expanded in the experiment, the
temperature must have risen.
Unfortunately, examples of such answers abound. We
.are not speaking of the excellent student or even of the
average student, of course. Yet it can be said without
exaggeration that for many students "qualitative" ques-
tions and problems present many more difficulties than
the derivation of formulas. The situation is especially
bad with the building of diagrams and sketching of exper-
iments. College instructors and lecturers often complain
of the low level of school instruction, but complaints' are
of no help. Hence, it is essential to develop a student's
creative thinking and ability to analyze physical phe-
nomena.
It was this that prompted me to draw on more than a
half-century of instruction at colleges in Leningrad and
compile the present collection of questions and problems.
7
, The book was conceived literally as a teaching aid; it is
intended to help the student in the physics course at the
freshman level. The main emphasis is on the use of dia-
grams and sketches. A drawing makes the essence of a
problem clearer and assists the development of "qualita-
tive" thinking. That is why I have chosen Michelangelo's
remarkable words for the epigraph to this work.
The questions and problems found here encompass prac-
tically all sections of the physics course studied in a
technical college. Since some colleges give greater stress
to certain topics, the book includes a number of ques-
tions and problems intended for a well-prepared student.
This feature makes it possible to use the book to some
extent in the physics departments of universities and
the physics and mathematics departements of teachers'
colleges. On the other hand, some problems require only
knowledge within the scope of secondary school, though
these are usually not considered in the school syllabus in
such form.
All questions and problems have detailed answers and
solutions. At times a variety of solutions are given. One
may be based on dimensionality considerations, while
another is achieved through direct integration. The major-
ity of answers and solutions are analyzed and discussed.
Sometimes practical applications are given to show how
and where the specific phenomena and laws are encoun-
tered.
In compiling this collection I did not aim at selecting
the most difficult or the least difficult questions and
problems. The range of difficulty is considerable. The
book is structured in such a way that all students, from
the well-prepared to the not-so-well-prepared , can use it.
If a student is not able to answer a question or solve a
problem without help, a careful study of the solution
will help him to master the theory involved and solve on
his own at first the simpler problems and then the more
complicated. A well-prepared student will be able to
solve most of the problems, hut even he will find it
helpful to compare his solution with the one given ill the
hook and to read the accompanying discussion of the re-
sults.
To answer the questions it is sufficient at times to read
the question, glance at the diagram, and write the approp-
riate formula. On the other hand, some problems require
8
Introduction 7
Questions and Problems 10
1. Fundamentals of Mechanics to
2. Molecular Physics and Thermodynamics 25
3. Electrostatics 42
4. Direct Current 54
5. Electromagnetism 67
6. Oscillatory Motion and Waves 80
7. Alternating Current 92
8. Optics 95
9. Atomic and Nuclear Physics t09
Answers and Solutions 121
1. Fundamentals of Mechanics 121
2. Molecular Physics and Thermodynamics t55
3. Electrostatics 188
4. Direct Current 213
5. Electromagnetism 233
6. Oscillatory Motion and Waves 254
7. Alternating Current 275
8. Optics 286
9. Atomic and Nuclear Physics 316
Postface 335
, A drawing is the source and soul
of every image and the root of every
science."
Michelangelo
Introduction
The student put down his record book and picked up an
examination card. Upon reading it, he gasped: "My God!
What will I do?" Judging by his face, one would think
be held at the very least a poisonous snake. The assign-
ment on the card read: "The velocity distribution of mol-
ecules; the Maxwellian curve." The student was not re-
quired to derive the formula or even write out the formu-
la. All he had to do was to draw the curve and explain its
physical meaning. Another student, in drawing the van
der Waals isotherm depicted something resembling a ca-
mel with two humps; moreover, the curve passed through
the origin. Still another student, while explaining the
idea behind the Stern experiment, made the outer cylin-
der rotate while the inner cylinder remained fixed. Fi-
nally, to the question of how the temperature of a gas
changes under adiabatic expansion a student gave the
following "reasonable" answer: since objects expand when
heated, and the gas expanded in the experiment, the
temperature must have risen.
Unfortunately, examples of such answers abound. We
.are not speaking of the excellent student or even of the
average student, of course. Yet it can be said without
exaggeration that for many students "qualitative" ques-
tions and problems present many more difficulties than
the derivation of formulas. The situation is especially
bad with the building of diagrams and sketching of exper-
iments. College instructors and lecturers often complain
of the low level of school instruction, but complaints' are
of no help. Hence, it is essential to develop a student's
creative thinking and ability to analyze physical phe-
nomena.
It was this that prompted me to draw on more than a
half-century of instruction at colleges in Leningrad and
compile the present collection of questions and problems.
7
, The book was conceived literally as a teaching aid; it is
intended to help the student in the physics course at the
freshman level. The main emphasis is on the use of dia-
grams and sketches. A drawing makes the essence of a
problem clearer and assists the development of "qualita-
tive" thinking. That is why I have chosen Michelangelo's
remarkable words for the epigraph to this work.
The questions and problems found here encompass prac-
tically all sections of the physics course studied in a
technical college. Since some colleges give greater stress
to certain topics, the book includes a number of ques-
tions and problems intended for a well-prepared student.
This feature makes it possible to use the book to some
extent in the physics departments of universities and
the physics and mathematics departements of teachers'
colleges. On the other hand, some problems require only
knowledge within the scope of secondary school, though
these are usually not considered in the school syllabus in
such form.
All questions and problems have detailed answers and
solutions. At times a variety of solutions are given. One
may be based on dimensionality considerations, while
another is achieved through direct integration. The major-
ity of answers and solutions are analyzed and discussed.
Sometimes practical applications are given to show how
and where the specific phenomena and laws are encoun-
tered.
In compiling this collection I did not aim at selecting
the most difficult or the least difficult questions and
problems. The range of difficulty is considerable. The
book is structured in such a way that all students, from
the well-prepared to the not-so-well-prepared , can use it.
If a student is not able to answer a question or solve a
problem without help, a careful study of the solution
will help him to master the theory involved and solve on
his own at first the simpler problems and then the more
complicated. A well-prepared student will be able to
solve most of the problems, hut even he will find it
helpful to compare his solution with the one given ill the
hook and to read the accompanying discussion of the re-
sults.
To answer the questions it is sufficient at times to read
the question, glance at the diagram, and write the approp-
riate formula. On the other hand, some problems require
8
