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E field between 2 wrinkled spheres, radial symmetry?

  1. May 12, 2013 #1
    [tex]\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}=[/tex]
    [tex]\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=[/tex]
    [tex]\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}[/tex]

    is a wrinkled sphere also an S2 object topologically though maybe different Euler characteristic? is this calculation correct since the field between 2 regular spheres has a radial term with symmetry? these spheres I read are used to model tumors

    thanks very much!
     
    Last edited: May 12, 2013
  2. jcsd
  3. May 19, 2013 #2
    this seems to be a good approach to design your own problems that are perhaps variations on standard ones, they do this at Princeton for instance
     
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