An Introduction to Vector Analysis For Physicists and by B. Hague D.SC., PH.D., F.C.G.I. (auth.)

By B. Hague D.SC., PH.D., F.C.G.I. (auth.)

The crucial adjustments that i've got made in getting ready this revised version of the e-book are the next. (i) Carefuily chosen labored and unworked examples were extra to 6 of the chapters. those examples were taken from classification and measure exam papers set during this college and i'm thankful to the college court docket for permission to take advantage of them. (ii) a few extra subject at the geometrieaI program of veetors has been integrated in bankruptcy 1. (iii) Chapters four and five were mixed into one bankruptcy, a few fabric has been rearranged and a few extra fabric extra. (iv) The bankruptcy on int~gral theorems, now bankruptcy five, has been improved to incorporate an altemative facts of Gauss's theorem, a treatmeot of Green's theorem and a extra prolonged discussioo of the type of vector fields. (v) the one significant switch made in what are actually Chapters 6 and seven is the deletioo of the dialogue of the DOW out of date pot funetioo. (vi) A small a part of bankruptcy eight on Maxwell's equations has been rewritten to offer a fuller account of using scalar and veetor potentials in eleetromagnetic idea, and the devices hired were replaced to the m.k.s. system.

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Extra resources for An Introduction to Vector Analysis For Physicists and Engineers

Sample text

Find, in a form similar to the above, the veetor equation of the eircle of radius R whieh lies in the same plane as C and is eoncentrie with C. 16. n = O. 35 PRODUCTS OF VECTORS A, B, C are the points with position veetors a, b, e respectiveIy. The pIane a contains the line OA and is perpendicular to the pIane OBC, where 0 is the origin. Similarly, the plane {J contains OB and is perpendicular to the plane OCA, and the pIane 'Y contains OC and is perpendicular to the plane OAB. Show that the pIanes a, {J, 'Y intersect in a line.

For a point in the field external to the conductor there is no current density and curl H= O. 8. Divergence of a Vector Product. g. in calculating the flux of e~ergy in an electromagnetic field, it is THE OP ERA TOR ss V AND ITS US ES required to find the veetor produet of two veetors and then to work out the divergence of the result. We thus seek to find div (A x B). 18, we write V = A x B = (A"Bz - AzB,,) i + (AzBiZ - AzBz) j + (AzB" - A"BiZ) k = ViZi + V"J + Vzk. 6, we find that . õViZ õV" õVz = - +õy- +OZ õx = BiZ (OAz _ oy OA,,) OZ + B" (OAiZ _ OA,) ÕZ OX + B.

Find the veetor equation of the line joining the points A and B with positian vectors i - 2j + k and i - j + 3k, respectiveIy, and show that the point P with position veetor i - Sj - Sk lies on AB. Find also the vector equation of the plane which passes through AB and the point C with position veetor k. 18. Prove that the points with position veetors - 2i + 2j, - i + j + 2k and i - j + 6k lie in a straight line and find the equation of the line. If this line interseets the line r = (s + 1) i + (1 - 3s) j + (e + 3s) k, where s is a parameter and e is a constant, prove that e = S.

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