# Vector and Tensor Calculus

• Sep 19th 2009, 06:47 AM
racnna
Vector and Tensor Calculus
Consider a sphere S of radius R with its center at the origin. Let x be a point on the surface. Using vector/tensor suffix notation, Evaluate

$\int\int_{S}$ $\frac{dA}{r}$ ; $r= \mid x-P \mid$

over the surface of the sphere, where P is a fixed point and integration is withr espect to x. COnsider separately the cases in which P lies inside or outside the sphere.

Hint: for P outside the sphere, expand 1/r in a taylor series expansion about $\mid x \mid$ and evaluate each term. For P inside the sphere, expand 1/r about $\mid P \mid$= 0.

you're supposed to use the 3 variable form of the taylor expansion.