# Math Help - unknown Gaussian surfaces?

1. ## wrinkled sphere Gaussian surface?

I invented this problem you don't have to do it, take 2 wrinkled spheres of opposite charge rhocharge2 and equal radius, volumerho1 of the spheres= $1+\frac{1}{2}sin(m\pi) sin(n\phi), m=6, n=5$ the spheres overlap in a region and the vector between the centers of the spheres is d. what is the electrical field between the 2 spheres. I'm curious if there are more Gaussian surfaces than spheres, cylinders, boxes....

2. ## Re: wrinkled sphere Gaussian surface?

$\oint E\cdot dA=|E|\int_{0}^{2\pi}\int_{0}^{\pi}(1+1/2sin6\theta\sin5\phi)^2sin\phi d\phi d\theta =|E|\int_{0}^{2\pi}(\frac{25}{99}sin^2(6\theta)+2) d\theta =|E|\frac{421\pi}{99}=$
$\frac{\rho_{q}}{\varepsilon o}\int_{0}^{2\pi }\int_{0}^{\pi }\int_{0}^{(1+\frac{1}{2}sin6\theta sin5\phi )}\rho^2sin(\phi )d\rho d\phi d\theta=$
$\frac{\rho_{q}}{\varepsilon o} \int_{0}^{2\pi }\int_{0}^{\pi } \frac{1}{198}(157-25cos12\theta )d\phi d\theta= \frac{157\pi\rho_{q}}{99\varepsilon o }... E=\rho_{q}\frac{157}{421\varepsilon o}...Er_{1}-Er_{2} = \frac{\rho_{q}d157}{421\varepsilon o}$ is the E field for wrinkled spheres similar to regular spheres? it should depend on radius and have some symmetry?

3. ## Re: unknown Gaussian surfaces?

this can't be correct because there should be a radial term? anyway these are used to model tumors, but biophysics is probably very competitive?