By Wolfgang Nolting
This textbook deals a transparent and complete creation to electrodynamics, one of many middle parts of undergraduate physics classes. the 1st a part of the e-book describes the interplay of electrical fees and magnetic moments by means of introducing electro- and magnetostatics. the second one a part of the e-book establishes deeper realizing of electrodynamics with the Maxwell equations, quasistationary fields and electromagnetic fields. All sections are followed by means of an in depth advent to the maths needed.
Ideally fitted to undergraduate scholars with a few grounding in classical and analytical mechanics, the e-book is more suitable all through with studying good points comparable to boxed inserts and bankruptcy summaries, with key mathematical derivations highlighted to assist realizing. The textual content is supported by way of various labored examples and finish of bankruptcy challenge units.
About the Theoretical Physics series
Translated from the popular and hugely winning German variations, the 8 volumes of this sequence hide the total middle curriculum of theoretical physics at undergraduate point. every one quantity is self-contained and gives the entire fabric important for the person direction subject. a variety of issues of particular options aid a deeper figuring out. Wolfgang Nolting is known for his sophisticated didactical variety and has been often called the "German Feynman" in reviews.
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Extra resources for Theoretical Physics 3: Electrodynamics
R/ dr C along the circle lying in the xy-plane with its center at the origin of coordinates and the radius R. 23 Are the following vector fields pure gradient-fields or pure curlfields? 1. 2. 3. 4. x2 y; cos z3 ; zy/. r/. r/. 1 1. 2. 3. 4. What do we call a distribution? Which requirements do define Dirac’s ı-function? List the most important properties of the ı-function. How does the three-dimensional ı-function read in curvilinear coordinates? 2 1. x/ be expanded as a Taylor series? 2. What does one understand by the approximate polynomial and the remainder term, respectively, of a Taylor series?
4 1. What does one understand by the average source density of the field E in the volume V? 46 1 Mathematical Preparations 2. 3. 4. 5. 6. 7. 8. How can one get from the average source density the divergence of the E-field? How does the general surface-integral representation of the nabla-operator read? r/ along the way C mean? What is denoted as vorticity of a vector field? Which connection does exist between circulation and curl? Formulate the line-integral representation of the curl! What is the general line-integral representation of the nabla-operator?
16 Calculate 1. ˛ r/ with spherical coordinates, 2. div er , grad diver , curl er , div e' , curl e# with spherical coordinates, 3. ˛ D const/. V/ over the closed surface of an arbitrary volume V always vanishes. r; t/ fulfill the relation curl E D @ B: @t At an arbitrary point of time t0 , B D 0 for all r. Show that for all times it must then hold div B D 0. 19 Given is an area F D Fez in the xy-plane: 1. F: circle with radius R around the origin, 2. F: rectangle with side lengths a and b. Show first by a direct calculation and then alternatively by use of the Stokes theorem that Z r dr D 2F : @F Interpret the result geometrically and find reasons why the relation is valid even for arbitrary areas F!