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Applications of Gauss's Law |
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Field due to a uniformly charged sphere of radius with a charge |
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Gaussian surface is a cylinder of radius  and length  . |
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By symmetry, the field is radial. Gaussian surface is a concentric sphere of radius  . The outward normals to the Gaussian surface is parallel to the field at every point. Hence For , |
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so that |
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The field outside the sphere is what it would be if all the charge is concentrated at the origin of the sphere.
For , a fraction of the total charge is enclosed within the gaussian surface, so that |
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The field inside is |
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Exercise |
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