Question

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..

Answer 1

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.