Step-by-step explanation:
To determine the force F of interaction between the half ring and the point charge, we can use the principle of superposition, which states that the total force on a point charge due to a collection of other charges is the vector sum of the individual forces that each of those charges would exert on the point charge if it were the only charge present.
First, we need to find the electric field at the center of curvature due to the charged half ring. The electric field at a point on the axis of a uniformly charged ring is given by:
E = kqz / (z^2 + R^2)^(3/2)
where k is Coulomb's constant, q is the linear charge density, z is the distance from the center of the ring to the point on the axis, and R is the radius of the ring.
At the center of curvature of the half ring, z = R, so the electric field is:
E = kq / (2R)
Next, we can use the electric field to find the force on the point charge q:
F = qE
Substituting the given values, we get:
F = (20 x 10^-9 C) x (9 x 10^9 N·m^2/C^2) x (1/20 cm)
F = 9 x 10^-3 N
Therefore, the force of interaction between the half ring and the point charge is 9 x 10^-3 N.
This force can also be interpreted as the force required to hold the point charge at the center of curvature against the electric field due to the charged half ring. It is an attractive force because the point charge is opposite in sign to the charged half ring.