Question

Two 10-cm -diameter charged rings face each other, 27cm apart. The left ring is charged to -16nC and the right ring is charged to +16nC.

Question 1) What is the magnitude of the electric field E ?   at the midpoint between the two rings?

Question 2) What is the magnitude of the force F ?   on a -1.0 nC charge placed at the midpoint?

Please answer both to two significant figures and I will rate.

Answer 1

The trick to this: Only the axial component (z-component) matters, everything else cancels out.

The second trick to this: The z-component contribution from both rings is the same, because both their relative position (relative to the center pint) and their charge are reversed.

So you only have to consider the z-component of a single point charge of magnitude 20 (nC) located at some point on one ring, and double it:
E_z = 2 * 8.988*10^9*(16e-9)*(1e-2)/(sqrt((1e-1^2 + 1e-1^2)^(3/2)
= 2.87616/sqrt(2)
= 2.03e3 (N/C), pointing left

F = e*E_z
= 1.6e-19 * 2.03e3
= 1.6*2.03*e-16
= 3.24e-16 (N), pointing right.