OBS: There is a negative sign, ##\vec{F}=-\nabla U##Delta2 said:I can't be fully rigorous here but i think the particle will experience a force upon it and this force will be towards the direction of change of the potential energy, i.e perpendicular to the plane of separation. (because it is ##\vec{F}=\nabla U##.)
Hence the component parallel to the plane of separation has no forces , so this component of the velocity is conserved.
If there is such field, then the potential energy wouldn't be constant ##U_1## in one space and ##U_2## in the other space, the potential energy will also vary along the direction parallel to the plane of separation.LCSphysicist said:But see, i think you agree with me there is fields that can produce a force parallel to the plane of separation.
This field is a consequence that the potential energy varies (from U_1 to U_2) in the direction perpendicular to the plane of separation.LCSphysicist said:Seems the question is imagining a field perpendicular to the plane.
The main components of a plane of separation problem are the two objects or entities that need to be separated, the distance between them, and any other relevant factors such as speed, direction, and external forces.
The distance between two objects in a plane of separation problem is typically calculated using mathematical equations, such as the distance formula or the Pythagorean theorem. In some cases, advanced tools such as radar or GPS may also be used to accurately measure the distance.
There are several factors that can affect the outcome of a plane of separation problem, including the speed and direction of the objects, external forces such as wind or gravity, and any potential obstacles or hazards in the path of the objects.
A plane of separation problem is typically solved using mathematical models and calculations to determine the optimal distance and direction for the two objects to maintain separation. Advanced technologies and tools may also be used to aid in the solution.
Plane of separation problems are commonly used in air traffic control to ensure safe distances between airplanes in flight. They can also be applied in other scenarios, such as navigation of ships at sea or coordination of vehicles in space missions.