Final answer:
The force exerted on a proton in the given scenario depends on the proton's position along the x-axis and is of quadratic nature, with the force direction being attractive towards the origin.
Step-by-step explanation:
The question asks about the force exerted on a proton when it is subject to a force given by f⟂ = -αx²i^, where α=12 N/m². To determine the force acting on the proton, we need the specific value of x, which is the position of the proton along the i^ (x-axis). Without the value of x, we cannot calculate the exact force. However, we know that the force is directed along the i^ axis (i.e., the x-axis) and is quadratic in nature, meaning that it increases with the square of the distance x. Additionally, since the force is negative, it is attractive and points towards the origin.
This type of force is encountered in certain potential fields, such as those used in physics to model the behavior of particles within electric, magnetic, or gravitational fields. The negative sign indicates that the force is directed opposite to the increase in x, hence it is attractive if x is positive (the proton is to the right of the origin), and repulsive if x is negative (the proton is to the left of the origin).