Posted by Andrew on Thursday, February 11, 2010 at 9:20pm.
Write an equation for the field along the axis as a function of x. When x = 0, the fields due to segmentes of the ring cancel ouut. As x -> infinity, the field falls with 1/x^2 behaior, so there has to be a maximum E for some x.
When adding up the fields due to each arc segment, you only have to add the x-components (along the axis) because the others will cancel out.
Here is what I get for E as a function of x:
E (x) = [k*Q /(x^2 + r^2)]*[x/sqrt(x^2+r^2)]
The second term in brackets is the cosine of the angle that defines the component in the x direction.
That function must be differentiated to find where the field is a maximum.
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