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8 a using gausss law of electrostatics find the electric...

Question: 8 a using gausss law of electrostatics find the electric...

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8. (a) Using Gausss law of electrostatics, find the electric field both inside and outside a thin metallic spherical shell of radius R. The electric charge is uniformly distributed over the shell with the charge surface density . Assume vacuun both inside and outside the shell and neglect its thickness. Provide a sketch showing the Gaussian surface of integration used. (b) Find the electrostatic potential of the system described in part (a) at all points of space (c) For an arbitrary electric charge distribution p(r) and the potential produced by this distribution, the electrostatic energy has the form Show, using Maxwells equation of electrostatics and the divergence the- orem, that this energy can be represented in terms of the electric field only, via where the integration is made over the full space Hint: When using the divergence theorem, show that the surface integral over the infinitely distant surface is vanishing due the radial dependence of E and p 6 (d) Using the second equation from part (c), find the electrostatic energy of the system in part (a)

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