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Problem of the Day #220: Uniform Spheres are Cool October 25, 2011

Posted by Albert in : potd , trackback

A sphere of radius $R$ has its center at the origin. There is a point $p$ outside the sphere at $(x,0,0)$ with a magical property value $v$ which affects the surrounding space as $f(v, d) = \frac{v}{d}$, where $v$ is the magical property value and $d$ is the distance from that point. Amazingly, you are informed that you can balance out the affect of point $p$ on the surface of the sphere with a point inside the sphere. Find that point’s position and magical property value.


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