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Math Help - unknown Gaussian surfaces?

  1. #1
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    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....
    Last edited by mathlover10; April 29th 2013 at 02:34 AM.
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    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?
    Last edited by mathlover10; May 1st 2013 at 11:39 PM.
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  3. #3
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    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?
    Last edited by mathlover10; May 2nd 2013 at 12:14 AM.
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