**Methodology for Applying Gauss's Law**

Step 1: | Identify the symmetry properties of the charge distribution. |

Step 2: | Determine the direction of the electric field, and a surface on which the magnitude of electric field is constant. |

Step 3: | Decide how many different regions of space the charge distribution determines. |

Step 4: | For each region of space, choose the Gaussian surface such such that the flux integral is either case (a) or case (b) above. |

Step 5: | Calculate the flux through the Gaussian surface. |

Step 6: | For each region of space, calculate the charge enclosed in the choice of the Gaussian surface for that region. |

Step 7: | For each region of space, equate the two sides of Gauss's law in order to find an expression for the magnitude of the electric field in that region of space. |

Step 8: | Graph the magnitude of the electric field as a function of the parameter specifying the Gaussian surface for all regions of space. |

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