By Snieder R.

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3). 24) Hint: consider the case where the radius is increased ( r > 0) and decreased ( r < 0) separately. 5. IS LIFE POSSIBLE IN A 5-DIMENSIONAL WORLD? 3: De nition of variables for the perturbed orbit of the earth. 24). e. mrv = m(r + r)(v + v). In what follows we will consider small perturbations and will retain only terms of rst order in the perturbation. This means that we will ignore higher order terms such as the product r v. 22) to show that ; Note that the perturbation of the centrifugal force does not depend on the number of spatial dimensions, but that the perturbation of the gravitational force does depend on N.

This de nition of sources and sinks is not restricted to uid ow. " Electrical eld lines originate at positive charges and end at negative charges. 4. 2) for a point charge in three dimensions vanishes except near the point charge at r = 0. Show also that the net ux through a small sphere surrounding the charge is positive (negative) when the charge q is positive (negative). The result we have just discovered is that the electric charge is the source of the electric eld. 12) In this expression (r) is the charge density, this is simply the electric charge per unit volume just as the mass-density denotes the mass per unit volume.

5. IS LIFE POSSIBLE IN A 5-DIMENSIONAL WORLD? 3: De nition of variables for the perturbed orbit of the earth. 24). e. mrv = m(r + r)(v + v). In what follows we will consider small perturbations and will retain only terms of rst order in the perturbation. This means that we will ignore higher order terms such as the product r v. 22) to show that ; Note that the perturbation of the centrifugal force does not depend on the number of spatial dimensions, but that the perturbation of the gravitational force does depend on N.

### A guided tour of mathematical physics by Snieder R.

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