To determine the position along the positive z axis where the electric field due to a uniformly charged circular loop is at its maximum, we follow these steps:

Expression for Electric Field (E):

The electric field E at a point along the z-axis for a charged circular loop can be expressed as:

Here, K is the Coulomb's constant, Q is the total charge, r is a constant involving charge distribution, x is the distance along the z-axis, and R is the radius of the loop.

Maximizing the Electric Field:

To find where E is maximum, we take the derivative of E with respect to x and set it to zero:

Solve for x :

Solving the equation from the derivative, we find:

Substitute Given Radius:
Given the radius , substituting into the expression for x :

Thus, the position along the positive z-axis where the electric field is maximum is at .