And as a unique addition to his fine book, he provides advice for selecting the optimal bat—a surprising bonus!
I think the book provides the foundation for change. In the present work a wide introduction to Josephson junction networks is provided. The Josephson equations are introduced by means of Ohta's semi-classical model and a simple description of the magnetic response of multiply connected superconductors is given.
The analysis of the magnetic response of Josephson junction networks is gradually built up from simple interferometers to three-dimensional lattices of superconducting devices. The analytic description of these systems may be applied when fabricating ultrasensitive vectorial magnetic field sensors and interpreting the low-field magnetic properties of superconducting granular systems.
The Discourse of Physics Author : Y. Through its detailed descriptions of the key semiotic resources and its analysis of the knowledge structure of physics, this book is an invaluable resource for graduate students and researchers in multimodality, discourse analysis, educational linguistics, and science education.
An explosion of new materials, devices, and applications makes it more important than ever to stay current with the latest advances.
Surveying the field from fundamental concepts to state-of-the-art developments, Photonics: Principles and Practices builds a comprehensive understanding of the theoretical and practical aspects of photonics from the basics of light waves to fiber optics and lasers. Providing self-contained coverage and using a consistent approach, the author leads you step-by-step through each topic. Each skillfully crafted chapter first explores the theoretical concepts of each topic and then demonstrates how these principles apply to real-world applications by guiding you through experimental cases illuminated with numerous illustrations.
Coverage is divided into six broad sections, systematically working through light, optics, waves and diffraction, optical fibers, fiber optics testing, and laboratory safety. A complete glossary, useful appendices, and a thorough list of references round out the presentation.
The text also includes a page insert containing 28 full-color illustrations. Containing several topics presented for the first time in book form, Photonics: Principles and Practices is simply the most modern, comprehensive, and hands-on text in the field. After exploring the rise of Si, MEMS, and NEMS in a historical context, the text discusses crystallography, quantum mechanics, the band theory of solids, and the silicon single crystal.
It concludes with coverage of photonics, the quantum hall effect, and superconductivity. Many numbers in the real world have even less accuracy. An automobile speedometer, for example, usually gives only two sig- nificant figures.
Even if you do the arithmetic with a calculator that displays ten digits, a ten-digit answer would misrepresent the accuracy of the results. Always round your final answer to keep only the correct number of significant figures or, in doubtful cases, one more at most. In Example 1.
Note that when you reduce such an answer to the appropriate number of significant figures, you must round, not truncate. Your calculator will tell you that the ratio of m to m is 1.
When we work with very large or very small numbers, we can show signifi- cant figures much more easily by using scientific notation, sometimes called powers-of notation.
The number 4. Note that in scientific notation the usual practice is to express the quantity as a number between 1 and 10 multiplied by the appropriate power of When an integer or a fraction occurs in an algebraic equation, we treat that number as having no uncertainty at all. We can consider this coefficient as having an infinite number of signifi- cant figures 2.
The same is true of the exponent 2 in v x2 and v 0x 2. A cheap digital watch that gives the time as a. A high-quality measurement is both precise and accurate. We are our answer to J, the energy gained or lost by a single atom given the value of the mass m; from Section 1.
TesT your undersTanding of secTion 1. But even a very crude estimate of a quantity often gives us useful information. Sometimes we know how to calculate a certain quantity, but we have to guess at the data we need for the calculation. Or the calculation might be too complicated to carry out exactly, so we make rough approxima- tions.
In either case our result is also a guess, but such a guess can be useful even if it is uncertain by a factor of two, ten, or more. Such calculations are called order-of-magnitude estimates. Most require guesswork for the needed input data. Even when they are off by a factor of ten, the results can be useful and interesting.
Could anyone carry thousand kilograms has a weight in British units of about a ton, that much gold? Would it fit in a suitcase? No human could lift it. Roughly what is the volume of this gold? The price per ounce has volume of a suitcase. Try the calcula- 1 mass of about 14 of 30 grams, or roughly 2 grams. Would this work? Hint: How many try day depends on the temperature, a scalar teeth are in your mouth?
Count them! But many other important quantities in physics have a direction associated with them and cannot be de- scribed by a single number. A simple example is the motion of an airplane: We must say not only how fast the plane is moving but also in what direction. The speed of the airplane combined with its direction of motion constitute a quantity called velocity.
Another example is force, which in physics means a push or pull exerted on a body. Giving a complete description of a force means describing both how hard the force pushes or pulls on the body and the direction of the push or pull. When a physical quantity is described by a single number, we call it a scalar quantity. Calculations that com- bine scalar quantities use the operations of ordinary arithmetic.
However, combining vectors requires a different set of operations. To understand more about vectors and how they combine, we start with the simplest vector quantity, displacement. Displacement is a change in the position of an object. Displacement is a vector quantity because we must state not only how far the object moves but also in what direction. We usually S represent a vector quantity such as displacement by a single letter, 1.
In this book we always print vector symbols in boldface a We represent a displacement by an arrow that italic type with an arrow above them. We do this to remind you that vector quan- points in the direction of displacement. When you handwrite a symbol for a vector, always write it with an arrow on top. We always draw a vector as a line with an arrowhead at its tip. It does not depend on the path taken, may be curved Fig.
Note that displacement is not related directly to the even if the path is curved. If the object were to continue past P2 and then return to P2 P1 , the displacement for the entire trip would be zero Fig. S A If two vectors have the same direction, they are parallel. If they have the same Path taken magnitude and the same S direction, they are equal, no matter where they are located P1 in space. These two displacements S S are equal, c Total displacement for a round trip is 0, even though they start at different points.
Two vector quantities are equal only when S they have the same magnitude and theSsame direction. Vector B in Fig. We define the negative of a vector as a vector having the same magnitude as Sthe original vector Sbut the opposite direction.
When two vectors A and B have opposite directions, whether their magnitudes are the same or not, we say that they are antiparallel. We usually represent the magnitude of a vector quantity by the same letter used for the vector, but inS lightface italic type with no arrow on top. For example, 1. An alternative notation same magnitude and the same or opposite is the vector symbol with vertical bars on both sides: direction.
Note that a vector can never be equalS to a scalar because they are P1 P3 P6 different kinds of quantities. For example, a displacement of 5 km might be represented in a di- and direction. S direction; BSis the agram by a vector 1 cm long, and a displacement of 10 km by a vector 2 cm long. S ment B. The final result is the same as if the particle S had started at the same The vector sum C WeS call dis- extends from Sthe of vector B. S placement C the vector sum, or resultant, of displacements A and B.
In vector addition we usually place the tail of the second matter in vector addition. In other words, tail to tail and constructing a parallelogram.
Figure S 1. In general, this S conclusion S is wrong; for the vectors shown in Fig. When the vectors are antiparallel S S Fig. To find the vector S sum of all three, inS Fig. The sum vector R extends from the tail of the first vector to the head of the last vector. The order makes no difference; Fig.
Vector addition obeys the associative law. We can subtract vectors as well S S as add them. The displacement S 2A is a displacement vector quan- but not its direction. SFor exam- changes its magnitude and reverses its direction. The direction S of F is the same - 3A S.
S as that of a because m is positive, and the magnitude of F is equal to the mass m S S S multiplied by the magnitude of a. The unit of force is the unit of mass multiplied - 3A is three times as long as A and points in the opposite direction. A cross-country skier skis 1. How far and in what direction is she from the starting point? This vector ad- dition amounts to solving a right triangle, so we can use the 1. We denote 0 1 km 2 km the direction from the starting point by the angle f the Greek letter phi.
The displacement appears to be a bit more than 2 km. In Section 1. Opposite side 2. There may be more than one correct an- When students were given a problem swer.
Common errors: 1. The head- In Section 1. Making measurements of a diagram offers only very limited accuracy, and 1. So we need a simple but general method for adding vectors. Remember that subtracting S S B from A is called the method of components. To define what we mean by the components of a vector A, we begin with Sa rect- angular Cartesian coordinate system S of axes Fig.
If we think of A as a displacement vector, we can regard A as the sum of a displacement parallel to the x-axis and a displacement parallel to the y-axis. We use the numbers Ax and Ay to tell us how much displacement there is parallel to the x-axis and how much there is S parallel to the y-axis, respectively. We can use the same idea for any vectors, not justS displacement y are the projections of the vector onto vectors.
The two numbers Ax and Ay are called the components of A. In this case, both Ax and Ay are positive. We can calculate the components of vector A if we know its magnitude A and its direction. In Fig. This is consistent with Eqs. But in Fig. Again, this is consistent with Eqs. In Bx Fig. If the angle of the vector is given from a different reference direction or you use a different rotation direc- tion, the relationships are different! Example 1. The figure indicates the signs of the components.
The angle we must use in Eqs. Equations 1. We can also reverse the gent. By applying the Pythagorean theorem to Fig. To S magnitude of vector A is decide which is correct, we have to look at the individual components.
Most pocket We always take the positive root. Equation 1. In x-axis and y-axis, as long as they are mutually perpendicular. Similarly, when both Ax and measured toward the positive y-axis as in Fig. Always Ay Ay draw a sketch like Fig. What is u? TAN button. Multiplying a vector by a scalar. Hence Eqs. Using components to calculate the vectorS sum resultant S of two or more S vectors.
The same is true for the y-components. In A and B using components. S Ay A Figure 1. WeS can introduce a z-axis perpendicular to the xy-plane; then in general a vector A has Ay components Ax, Ay, and Az in the three coordinate directions. Also, Eqs. It may be the magnitude of the vector sum, the direction, or by Eqs.
Draw the vector sum R from 2. Add the individual x-components algebraically including the tail of the first vector at the origin to the head of the last signs to find Rx, the x-component of the vector sum. Do the vector. S Use your sketch to estimate the magnitude and direction same for the y-components to find Ry.
See Example 1. Calculate the magnitude R and direction u of the vector sum by lation: Eqs. Rx execuTe the solution as follows: evaLuaTe your answer: Confirm that your results for the magni- 1. Find the x- and y-components of each individual vector and tude and direction of the vector sum agree with the estimates you record your results in a table, as in Example 1. If a vector is made from your sketch.
Three players on a reality TV show are brought to the center of a immediately, but the winner first calculates where to go. What large, flat field. Each is given a meter stick, a compass, a calcula- does she calculate?
See S Figure 1. The table below shows the components of all the displacements, the addition of the components, and the other cal- Distance Angle x-component y-component We may now mates. Notice how drawing the diagram in Fig. Its only pur- pose is to point—that is, to describe a direction in space. Unit vectors provide a convenient notation for many expressions involving components of vectors. Unit vectors nd, ne, and kn point in the If not all of the vectors lie in the xy-plane, then we need a third component.
Then Eqs. Any vector can be expressed in terms en of its x-, y-, and z-components S From Eq. We can use Eq. It will prove useful for calculations with many other vector quantities. We can also express many physical relationships by using products of vectors.
The first, called the scalar product, yields a result that is a scalar quantity. The second, the vector product, yields another vector. Because S S S S. S ofS this notation, the scalar product is also called the dot product.
Although A and B are vectors, the quantity A B is a scalar. S direction of A and is equal to B cos f. S S The scalar product is a scalar quantity, not a vector, and it may be positive, negative, or zero. A cos f Fig. The scalar product S B of two perpendicular vectors S is always S zero.
The scalar product obeys the commutative law of multiplication; A the order of the two vectors does not matter. We can calculateS the scalar S f components of A and B. All unit vectors have magnitude 1 and are S A Using Eq. From Eqs. Thus the scalar product of two vectors is the sum of the products of their respec- tive components. The scalar product S gives S a straightforward way to find the angle f between any two vectors A and B whose components S S are known.
In this case we can use Eq. Find the scalar product A B of the two vectors in Fig. Find the angle between the vectors 1. Our target variable is the angleS f Sbetween them Fig. AS and B. Thus AB As the name suggests, the vector product is itself a vector.
The two vectors then lie in a plane. S AB sin f. That is, the vector 4 Thumb points in direction of B : A. S S S S product of two parallel or antiparallel vectors is always zero. In particular, the 5 B : A has same magnitude as A : B vector product of any vector with itself is zero. To see S. S theSdifference between these two expressions, imagineSthat weS vary the angle between A and B while keeping their magnitudes constant.
When A and B are parallel, the magnitude S of S the vector product will be zero and the scalar product will be maximum. When A and B are perpendicular, the magnitude of the vector product will be maximum and the scalar product will be zero. There are always two directions perpendicular to a given plane, S one on each S side of the plane. We choose S which of these is the direction of A S : B as follows. Imagine S rotating vector A about the perpendicular line until S A is aligned S with B, choosing the smaller of the two possible angles between A and B.
Curl the fingers of your right hand around the perpendicular line so that your fingertips point S S in the direction of rotation; your thumb will then point in the direction of A : B. The result is a vector that is opposite to the vector A : B. Just as we did for the scalar product, we can give a geometrical interpretation S S Magnitude of A : Component of B S of the magnitude S of the vector product.
From Eq. SFigure 1. Note that Fig. Magnitude of A : B also equals B A sinf. S S Magnitude of B : Component of A S using components to calculate the vector Product aperpendicular to Bb S S If we know the components of A and B, we can calculate the components of the S A sinf vector product by using a procedure similar to that for the scalar product. First B we work out the multiplication table for unit vectors nd , ne , and kn , all three of which f are perpendicular to each other Fig.
The vector product of any vector S A with itself is zero, so. Using Eqs. Evaluating these by using the multiplication table for the nd x unit vectors in Eqs. If S youS compare S Eq. With the axis system of Fig. In fact, all vector prod- ucts of unit vectors nd , ne , and kn would have signs opposite to those in Eqs.
So there are two kinds of coordinate systems, which differ in the signs of the vec- tor products of unit vectors. Note that A points S along the x-axis, so its only nonzero which will provide a check of our calculations. For B, Fig. Vector B lies in the xy-plane. S evaLuaTe: Both methods give the same result.
Depending on the C situation, one or the other of the two approaches may be the more z convenient one to use. For each of the following situations, state what the value Sof f must be. In each situation there may be more than one correct answer. Physical quantities and units: Three fundamental physical quantities are mass, length, and time.
The corresponding fundamental SI units are the kilo- gram, the meter, and the second. Derived units for other physical quantities are products or quotients of the basic units. Equations must be dimensionally consistent; two terms can be added only when they have the same units. See Examples 1. Significant figures: The accuracy of a measure- Significant figures in magenta ment can be indicated by the number of significant figures or by a stated uncertainty.
The significant C 0. When only The negative of a vector has the same magnitude but points in the opposite direction. The unit vectors nd , ne , and kn , aligned with the en x x-, y-, and z-axes of a rectangular coordinate sys- O nd Axnd tem, are especially useful.
The scalar S S S A product of two perpendicular vectors is zero. The vector product of two parallel or antiparallel vectors is zero. Solution bridging Problem vecTorS on The roof. An air-conditioning unit is fastened to a roof that slopes at an angle 1. Its weight is a force F on the air conditioner that is directed vertically downward. One newton, or 1. It is equal to 0. This problem involves vectors and components. What are the part a. Which aspect s of the weight vector mag- tion? Hint: Check your sketch.
Make sure your answer has the correct number of significant target variable for part a? Which aspect s must you know to figures. Use the definition of the scalar product to solve for the target 2.
Make a sketch based on Fig. Draw the x- and y-axes, variable in part b. Again, use the correct number of signifi- choosing the positive direction for each. Did your answer to part a include a vector component whose 3. Is variables.
There are two ways to find the scalar product of two vectors, execuTe one of which you used to solve part b. Check your answer by 4. Use the relationship between the magnitude and direction of a repeating the calculation, using the other way. Do you get the vector and its components to solve for the target variable in same answer? CP: Cumulative problems incorporating material from earlier chapters.
CALC: Problems requiring calculus. How many do we need to prove a theory? SWhat must be true about Q1. Is this possible? Why or why not? National Institute of Standards and Technology from the past to the future. Does that make time a vector quantity?
Even after careful cleaning, these national Q1. Does this apparent increase have cosine for that axis. If a train travels km from Berlin sium clock could you use to define a time standard? Is it correct to write paper with an ordinary ruler. In each case, give the reason Q1. Suppose another student for your answer. Explain why this cannot be right. Give an example that illustrates the general rule Q1. Can you choose vectors A, B, and C such that these two and 10 cm to the right of the center of the target.
If so, give S an example. The contest judge Hint: Do not look for an elaborate mathematical proof. Consider says that one of the archers is precise but not accurate, another the definition ofS the S direction of the cross product. Which description applies to which archer? What can you say about Ax and Ay?
Justify your answers. What length restrictions are required for Section 1. Starting with the definition 1 in. The radius of the Earth is km.
According to the label on a bottle of salad dressing, the Q1. Using only the conver- to tell airline pilots in which direction they are to fly. How many nanoseconds does it take light to travel 5. This result is a useful quantity to remember. Can the 1. The density of mercury is What is this value magnitude of a vector be less than the magnitude of any of its in kilograms per cubic meter?
The most powerful engine available for the classic Q1. Chevrolet Corvette Sting Ray developed horsepower and had Why? Express this displacement in of another?
A square field measuring Which of these of 1. An acre has an area of 43, ft2. If a lot has an quantities could the plausibly represent? How many years older will you be 1. Assume a day year. How many kernels of corn does it take to fill a 4-L soft 1. While driving in an exotic foreign land, you see a speed limit drink bottle? Take that about four kernels fill 1 cm3. How many miles 1. One furlong is 18 mile, and a fortnight is 14 days.
A furlong originally referred to the length of a plowed furrow. A certain fuel-efficient hybrid car gets gasoline mileage of as is typical, each of them breathes about cm3 of air with each Use the ters of the space station have to be to contain all this air? The following conversions occur frequently in physics hide her from sight.
Estimate the monetary value of this pile. The and are very useful. Estimate that the heart pumps 50 cm3 of blood with 1. In the fall of , scientists at Los each beat.
Alamos National Laboratory determined that the critical mass of 1. You are using water to dilute small amounts of chemicals neptunium is about 60 kg. The critical mass of a fissionable in the laboratory, drop by drop. How many drops of water are in a material is the minimum amount that must be brought together to 1.
Hint: Start by estimating the diameter of a drop start a nuclear chain reaction. Neptunium has a density of of water. What would be the radius of a sphere of this material that has a critical mass? Section 1. S For the vectors A and Figure e1. Express this S S. How many grams per day drawing to find the magnitude should a kg adult receive? Use your See also 1. Bacteria vary in size, but a diameter of Exercise 1.
What are the volume in cubic centimeters approach. A postal employee and surface area in square millimeters of a spherical bacterium of that size? Consult Appendix B for relevant formulas. Determine the magnitude and direc- tion of the resultant displacement by drawing a scale diagram. With a wooden ruler, you measure the length of a rectan- gular piece of sheet metal to be 16 mm. With micrometer calipers, Figure e1. Determine the percent 2. There are Express each approximation of p to six significant N.
A spelunker is surveying a cave. She follows a passage 1. S S she finds herself back where she started. See also Problem 1. Compute the x- and y-components of the vectors A, B, C, Fig.
Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
Course Technology. Gary B. Shelly , Harry J. American Chemical Society. Since Free ebooks since ZLibrary app. Plz, I need it. Volume
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