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Acceleration of Gravity/Divergence Theorem

Acceleration of Gravity. See attached file for full problem description.

Find the acceleration of gravity g for the following mass distribution. The mass distribution consists of an infinitely long "wire" of radius a running along the z axis, surrounded by empty space then by a hollow cylinder with inner radius b and outer radius c, also centered on the z axis. Both the inner wire and the outer cylinder have density p. In effect this looks like a coaxial cable oriented along the z axis. Be sure to describe the direction as well as the magnitude of g in all of the different regions: within the inner wire, between it and the hollow cylinder within the cylinder and outside the cylinder.


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The gravitational force is an inverse square force (that is conservative), therefore we can use Gauss law to calculate the "Gravitational Field" at distance r from the center of the earth:

That is, the flux of the gravitational field through a closed surface is proportional to the mass enclosed by this volume. The negative sign reflects the fact that the field lines are always going ...

Solution Summary

The solution calculates the acceleration of gravity with reference to an infinitely long wire.