Posted by Andrew on .
Consider a charged ring of radius 43.4 cm and total charge 18 nC.
We are interested in the electric field a perpendicular distance z away from the center of the ring.
At what distance from the center of the ring does the electric field become maximum
..so E=kQ/(x^2)at a maximum distance...
how would i solve for x without E? ..sorry, im really confused with this question..

Physics (2) 
drwls,
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 xcomponents (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.