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Related Rates involving circular ring 
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#1
Oct2012, 12:52 AM

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1. The problem statement, all variables and given/known data
A circular ring of wire of radius r_{0} lies in a plane perpendicular to the xaxis and is centered at the origin. The ring has a positive electric charge spread uniformly over it. The electric field in the xaxis direction, E, at the point given by E=kx/((x^2 +r_{0}^2)^(3/2)) for k>0 at what point on the xaxis is greatest? least? 2. Relevant equations 3. The attempt at a solution so the only thing i could really think of to do is take the derivative. the circle itself isn't changing so I assumed r0 is a constant as well as k. [itex]E'=(k(x^2 + r_{0}^2)^(3/2)  3kx^2√(x^2 +r_{0}^2))/((x^2 +r_{0}^2)^(3/2))[/itex] after this i find the critical points 0=(k(x^2 + r_{0}^2)^(3/2)  3kx^2√(x^2 +r_{0}^2))/((x^2 +r_{0}^2)^(3/2)) 0=(x^2 +r0^2)^(3/2) 3x^2√(x^2+r0^2) im not sure what do here. I feel like I should have solved for r0 in terms of x, but im not sure. 


#2
Oct2012, 12:56 AM

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#3
Oct2012, 09:51 AM

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Once you find and pull out the greatest common factor of the terms in the numerator, the numerator will be a product of factors, and it will be easy to find the values of x for which E'(x) = 0. 


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