- #1
Taylor Smith
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Homework Statement
I'm working on a generalization of gravitation to n dimensions. I'm trying to compute gravitational attraction experienced by a point mass y due to a uniform mass distribution throughout a ball of radius a -- B(0, a).
Homework Equations
3. The Attempt at a Solution [/B]
I've determined an integral that expresses this problem, (ignoring the constants outside the integral) but I'm unsure how to evaluate it.
I have $$A = \int_{B(0,a)} \frac{x - y}{||x - y||^n} dvol_n(x)$$
I believe this can be expressed as a function of x_n, thus I've further simplified to
$$A = \int_{B(0,a)} \frac{x_n - r}{||x - re_n||^n} dvol_n(x)$$
where $r$ is the norm of y, and e_n is the unit vector that is 0 in all but the nth position. I'm unsure how to proceed with this integral. I'm trying to express it in terms of only a and r.