Download 1000 Solved Problems in Modern Physics by Ahmad A. Kamal PDF

By Ahmad A. Kamal

This booklet essentially caters to the desires of undergraduates and graduates physics scholars within the region of recent physics, particularly particle and nuclear physics. Lecturers/tutors may perhaps use it as a source booklet. The contents of the ebook are in keeping with the syllabi presently utilized in the undergraduate classes in united states, U.K., and different international locations. The booklet is split into 10 chapters, every one bankruptcy starting with a short yet enough precis and worthwhile formulation, tables and line diagrams through various usual difficulties important for assignments and tests. precise recommendations are supplied on the finish of every chapter.

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Example text

7 for the line integral. 10 Use the divergence theorem A . ds = ∇. A dν ∂ 3 ∂ ∂ 3 x + y + z3 ∂x ∂y ∂z = 3x 2 + 3y 2 + 3z 2 = 3(x 2 + y 2 + z 2 ) = 3R 2 But ∇. A = A . (dx iˆ + dy ˆj + dz k) R 4 dR = A . 3 Solutions 37 Put x = R cos θ, dx = −R sin θ dθ, y = R sin θ, dy = R cos θ, z = 0, 0 < θ < 2π A . 12 (a) ∇ × (∇Φ) = =i j k ∂ ∂ ∂ ∂ x ∂ y ∂z ∂Φ ∂Φ ∂Φ ∂ x ∂ y ∂z 2 ∂ 2Φ ∂ Φ − ∂ y∂z ∂z∂ y ∂ 2Φ ∂ 2Φ − ∂ x∂z ∂z∂ x −j +k ∂ 2Φ ∂ 2Φ − ∂ x∂ y ∂ y∂ x =0 because the order of differentiation is immaterial and terms in brackets cancel in pairs.

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 .

The order of a differential equation is that of the highest derivative in it. The degree of a differential equation which is algebraic in the derivatives is the power of the highest derivative in it when the equation is free from radicals and fractions. Differential equations of the first order and of the first degree Such an equation must be brought into the form Mdx + N dy = 0, in which M and N are functions of x and y. 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.

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