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Gauss's Law Problem - Spherical Shell with Non-uniform Charge
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[QUOTE="JollyOlly, post: 4636575, member: 239360"] Your first equation is correct and not only does it tell you the total charge on the inner surface of the shell, it also tells you the total charge inside [I]any[/I] concentric sphere of any radius inside the shell. (Can you see why?) Where you have gone wrong is to introduce the equation for the volume of a sphere. This is not relevant as the charge density within the shell is not uniform. What you must do is differentiate the first equation to find the total charge within a thin shell of thickness δ[I]r[/I]; then divide by the volume of the shell to get the charge per unit volume. [/QUOTE]
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Gauss's Law Problem - Spherical Shell with Non-uniform Charge
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