February 19, 2017

Homework Help: Physics and Calculus

Posted by Sandra on Monday, February 15, 2010 at 6:40am.

Consider a charged ring of radius 27 cm and total charge 15 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 = kQz/ (z^2+R^2)^3/2

I understand that we would need to differentiate this equation and solve for when it equals zero..but I'm having real hard time differentiating. Could someone help me out?

This is what I have so far...

E'ring = kQ (z/[(z^2 +R^2)^3/2])
= {{1/(z^2+R^2)^3/2}} - {{z(z^2+R^2)^1/2}} / {{(z^2+R^2)^3}}

This is what I got by using the product rule. But I don't know how to get rid of the constant R from the equations and or how to simplify in such a way that I would be able to solve for Z.

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