By Roger James Elliott, Alan Frank Gibson
Elliott and Gibson's vintage creation to stable nation physics.
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Additional resources for An Introduction to Solid State Physics and Its Applications
Sample text
GRAVITY Çà x−x origin to an arbitrary point x , the collective gravitational field due to all the material particles in a volume V becomes an integral, ÖÖ x ................................... ......... ....... ....... ...... .. ... . .. .. ... .... .... . ... .... .... ...... . . . ..... ...... ........... ¨¨x 0 The vectors involved in calculating the field in the position x. g( x) = −G x−x ρ(x ) d V . 13) Note that the integrand has a singularity at x = x (when ρ(x) = 0).
6), and renaming the integration variables, the total force by which a mass distribution ρ2 in the volume V2 acts on a mass distribution ρ1 in V1 becomes, 12 = −G V1 x1 − x2 ρ1 ( x 1 )ρ2 ( x 2 ) d V1 d V2 . 14) Newton’s third law is fulfilled, 12 = − 21 , because the integrand is antisymmetric under exchange of 1 ↔ 2 due to the first factor. Consequently, the force from a mass distribution acting on itself vanishes, as it ought to. For if this self-force did not vanish a body could, so to speak, lift itself by its bootstraps.
Field lines around a point particle all come in from infinity and converge upon the particle. 34 Ö 3. GRAVITY ÇÃ x−x origin to an arbitrary point x , the collective gravitational field due to all the material particles in a volume V becomes an integral, ÖÖ x ................................... ......... ....... ....... ...... .. ... . .. .. ... .... .... . ... .... ....
