- #36
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For this problem, the symmetry argument is a mathematical one, in that for every component of ## \vec{E} ## that points radially outward, there is a corresponding point on the opposite side of the ring where the radially outward component will cancel it. The other way of looking at the symmetry is to say that if the resultant ## \vec{E} ## has a radially outward component, there is no favored direction, and thereby the radially outward component must be zero. I like the first approach better, but in any case, it pays to be able to use all the tools that are available in solving problems, and symmetry is one of those tools.