(adsbygoogle = window.adsbygoogle || []).push({}); 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 x-axis and is centered at the origin. The ring has a positive electric charge spread uniformly over it. The electric field in the x-axis direction, E, at the point given by

E=kx/((x^2 +r_{0}^2)^(3/2)) for k>0

at what point on the x-axis 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.

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# Related Rates involving circular ring

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