An infinitely long straight insulated rod (radius R) is uniformly charged with a constant charge density...

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An infinitely long straight insulated rod (radius R) is uniformly charged with a constant charge density p and simultaneously has a constant linear charge density . Apply Gauss's law to calculate the electric flux density both inside and outside the rod. a) Consider the possible directions of the electric field components given the symmetry, and then formulate the appropriate Gaussian surface S. b) Sketch a diagram of the Gaussian surface, and draw vectors for the flux density and surface element in different parts of the surface. c) Use Gauss's law to derive an expression for the electric flux density as a function of the distance r from the rod's central axis for all values where r > 0. Answers: For r < R: D(r) = pr 2 For r > R: D(r) = PR 2r 2 An infinitely long straight insulated rod (radius R) is uniformly charged with a constant charge density p and simultaneously has a constant linear charge density . Apply Gauss's law to calculate the electric flux density both inside and outside the rod. a) Consider the possible directions of the electric field components given the symmetry, and then formulate the appropriate Gaussian surface S. b) Sketch a diagram of the Gaussian surface, and draw vectors for the flux density and surface element in different parts of the surface. c) Use Gauss's law to derive an expression for the electric flux density as a function of the distance r from the rod's central axis for all values where r > 0. Answers: For r < R: D(r) = pr 2 For r > R: D(r) = PR 2r 2