Potential EnergyPotential energy is energy which results from position or configuration. An object may have the capacity for doing work as a result of its position in a gravitational field (gravitational potential energy), an electric field (electric potential energy), or a magnetic field (magnetic potential energy). It may have elastic potential energy as a result of a stretched spring or other elastic deformation. 
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Potential Energy FunctionIf a force acting on an object is a function of position only, it is said to be a conservative force, and it can be represented by a potential energy function which for a onedimensional case satisfies the derivative condition The integral form of this relationship is which can be taken as a definition of potential energy. Note that there is an arbitrary constant of integration in that definition, showing that any constant can be added to the potential energy. Practically, this means that you can set the zero of potential energy at any point which is convenient. 
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Potential Energy Concept

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Negative Signs in Potential

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Potential Energy DerivativeIf the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential. 
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Potential Energy IntegralIf the force is known, and is a conservative force, then the potential energy can be obtained by integrating the force. 
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Conservative ForceA conservative force may be defined as one for which the work done in moving between two points A and B is independent of the path taken between the two points. The implication of "conservative" in this context is that you could move it from A to B by one path and return to A by another path with no net loss of energy  any closed return path to A takes net zero work. A further implication is that the energy of an object which is subject only to that conservative force is dependent upon its position and not upon the path by which it reached that position. This makes it possible to define a potential energy function which depends upon position only. 
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