(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a charged ring of radius 20.6 cm and total charge 12 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?

Hint: The field for a ring of charge is:

Ering = (1/4 pi eo) (zQ/(z^2+R^2)^(3/2))

2. Relevant equations

3. The attempt at a solution

When x = 0, the fields due to segments of the ring cancel out. As x -> infinity, the field falls with 1/x^2 behavior, 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.

1) is this right so far

2) if so how do I differentiate this

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# Homework Help: Charged Ring

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