By Ahmad A. Kamal

ISBN-10: 3642043321

ISBN-13: 9783642043321

This e-book essentially caters to the desires of undergraduates and graduates physics scholars within the quarter of recent physics, in particular particle and nuclear physics. Lecturers/tutors might use it as a source ebook. The contents of the e-book are in response to the syllabi at the moment utilized in the undergraduate classes in united states, U.K., and different nations. The booklet is split into 10 chapters, every one bankruptcy starting with a short yet enough precis and useful formulation, tables and line diagrams via numerous usual difficulties important for assignments and checks. precise options are supplied on the finish of every chapter.

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B) = 0 Subtracting, B . (∇ × A) − A . (∇ × B) = 0 Now ∇ . ( A × B) = B . (∇ × A) − A . (∇ × B) Therefore ∇ . ( A × B) = 0, so that ( A × B) is solenoidal. 5 (a) Curl {r f (r )} = ∇ × {r f (r )} = ∇ × {x f (r )iˆ + y f (r ) ˆj + z f (r )k} ˆj iˆ kˆ ∂ ∂ ∂ ∂f ∂f = z −y = ∂x ∂y ∂z ∂y ∂z x f (r ) y f (r ) z f (r ) But ∂f ∂x = ∂f ∂r ∂r ∂x ∂f = yrf ∂y Similarly respect to r . r F(r ) = 0 ∂(x F(r )) ∂(y F(r )) ∂(z F(r )) + + =0 ∂x ∂y ∂z ∂F ∂F ∂F F+x +F+y +F +z =0 ∂x ∂y ∂z ∂F y ∂F z ∂F x +y +z =0 3F(r ) + x ∂r r ∂r r ∂r r x 2 + y2 + z2 ∂F =0 3F(r ) + ∂r r But (x 2 + y 2 + z 2 ) = r 2 , therefore, ∂∂rF = − 3F(r) r Integrating, ln F = −3 ln r + ln C where C = constant C ln F = − ln r 3 + ln C = ln 3 r r Therefore F = C/r 3 .

Type I variables separable When the terms of a differential equation can be so arranged that it takes on the form (A) f (x) dx + F(y) dy = 0 where f (x) is a function of x alone and F(y) is a function of y alone, the process is called separation of variables and the solution is obtained by direct integration. (B) where C is an arbitrary constant. 1 Basic Concepts and Formulae 17 Equations which are not in the simple form ( A) can be brought into that form by the following rule for separating the variables.

Fig. 91 If a soap film is stretched between two circular wires, both having their planes perpendicular to the line joining their centers, it will form a figure of revolution about that line. At every point such as P (Fig. 5), the horizontal component of the surface of revolution acting around a vertical section of the film will be constant. Find the equation to the figure of revolution. 92 Prove that the sphere is the solid figure of revolution which for a given surface area has maximum volume.

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