Charge is uniformly distributed around a ring of radius R= 2.40 cm and the resulting electric field magnitude E is measured along the ring's central axis ( perpendicular to the plane of the ring). At what distance from the ring's center is E maximum?
In this question, I end up with E(total) = (q * z) / 4*Pi * e * (R^2 + z^2)^3/2
where e is the permittivity constant, and z is the distance from the ring's center along the axis, and q is the charge on the ring
I believe to find E maximum, I need to differentiate and set the derivative equal to zero, but I only get the minimum E which is at the ring's center. I'm not sure how to determine the maximum. the derivative I get is as follows:
dE = -3*q*z / 4*Pi*e*(R^2 + z^2)^5/2
Could you please double check my method and determine what I am missing to solve z for the maximum E?