Ring of Charge-how to maximize the Electric Field

[lu6cifer]

Ring of Charge--how to maximize the Electric Field

A thin nonconducting rod with a uniform distribution of positive charge Q is bent into a circle of radius R. The central perpendicular axis through the ring is a z-axis, with the origin at the center of the ring.


(c) In terms of R, at what positive value of z is that magnitude maximum (of the Electric Field)?




After going through the integration, the equation for a ring of charge is

k*(Qz / (z²+R²)^3/2))





Edit: So, with some help, I realized that to maximize the function, I'd have to differentiate...
But what am I differentiating with respect to? z? r? And I know k is a constant; are everything else non-constants?

 

[Redbelly98]

You're looking for the value of z which maximizes the function, while the size of and charge on the ring are constants.

 

[tomcue]

To maximize the electric field for a ring of charge, you would differentiate the equation with respect to z, as z is the variable that determines the distance from the center of the ring. The other variables, such as R and Q, are constants in this scenario.

To find the maximum value of the electric field, you would set the derivative equal to zero and solve for z. This will give you the value of z at which the electric field is maximized. However, keep in mind that this maximum value will also depend on the values of R and Q.

Additionally, it is important to note that the electric field will also be affected by the distance of the point of interest from the ring. So, while maximizing the electric field at a certain distance from the ring is important, it is also essential to consider the distance of the point from the ring in order to fully understand the behavior of the electric field.