Final answer:
The force exerted on the proton cannot be determined with the information provided as the value of position 'x' is necessary. The equation indicates a force dependent on the square of the position 'x' in the negative direction of the x-axis.
Step-by-step explanation:
The force exerted on a proton in the context provided is a specific example of a force that varies with position. The force equation given is −αx²⇒, with α being a constant equal to 12 N/m². However, without the specific value of x, the position of the proton, we cannot calculate the exact magnitude of this force. Generally, this equation indicates that the force is proportional to the square of the position along the i direction (or the x-axis) and acts in the negative direction of the axis.
In terms of additional examples provided, a uniform magnetic field interacting with a moving charge, such as a proton, will result in a magnetic force. This force is calculated using the equation F = qvBsin(θ), where q is the charge of the proton, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field. The right-hand rule allows us to determine the direction of the force relative to the directions of the velocity and the magnetic field.