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In what form is potential energy stored in a system? I understand that when we do work we transfer some amount of energy to the system it can be seen as kinetic energy or potential energy. Suppose we lift a particle by doing mgh work on the particle. How will this energy be stored in the particle. In case of providing energy by heating the motion of the particles increase but what happens when the potential energy is increased...?

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    $\begingroup$ The energy won't be stored in the particle but in the field, but classical mechanics can not describe this. $\endgroup$ – CuriousOne Jun 1 '16 at 10:40
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    $\begingroup$ Also, note that it makes no sense to refer to the potential energy of a single particle. PE is defined for pairs of interacting particles. This doesn't much help answer your question, but should help in thinking about energy. $\endgroup$ – garyp Jun 1 '16 at 10:49
  • $\begingroup$ Think about refining your question to one system, otherwise its too broad. For example . "Suppose we lift a particle by doing mgh work on the particle. How will this energy be stored in the particle". In this case the p.e is not stored in the particle itself, but in another system, say adding heat to a gas containing vibrating molecules, ( an S.H.O. in effect), it might be. $\endgroup$ – user108787 Jun 1 '16 at 10:50
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Suppose we lift a particle by doing mgh work on the particle. How will this energy be stored in the particle?

we normally lift a body (designated by a point on paper-called a particle) of mass m and do some work-

It means something is operating to prevent this action /or oppose our action of 'lifting' that's why one has to do work-

meaning thereby that a force is being applied on the body and the point of application of the force gets displaced (in the direction/or opposite to the resisting action)

Therefore the energy of the body is being raised by application of the "lifting action" as the amount of work done on the body must be stored somewhere and its stored in the new position of the body in space-that is at a height h from its initial position.

One can say that if a body is in the field of force (the present case being gravitational field of force) its position naturally defines an energy of the type 'potential' which denotes the potential to perform work in the field/space.

If we keep water on a raised container ,the water has the potential to do work 'due to its position' in the gravitational field -on earth.

It can generate electrical energy if it falls on blades of a turbine attached to a generator of electrical energy.

Similarly if one takes a charged particle in an electric field (spread out in space)-

The amount of work done on it by changing its position in such a field gives rise to potential energy of the body.

Or we are talking of potential defined in a force field and as per its field intensity its scalar characteristic 'the potential' can also be defined and a change in potential can lead to a work being done by a body or the work being done on the body.

Therefore if one looks up the body and measures its temperature or observes its other features -one will not find evidence of the work done in its internal energy-

rather if he observes the field intensities and its variation along with potential defined at each point in space -he can estimate the potential energy of a body depending upon the type of field one is dealing with.

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