Potential energy is a fundamental concept in physics, crucial for mastering topics like Mechanics and Electromagnetism in competitive exams such as JEE. It represents the energy stored within an object or system due to its position or configuration. Unlike kinetic energy, which is energy of motion, potential energy is the 'stored' capacity to do work.

Potential energy (PE) is the energy an object possesses because of its position relative to some zero point. It's often associated with conservative forces, where the work done by the force in moving an object between two points is independent of the path taken. This stored energy can be converted into kinetic energy or other forms of energy.

Several types of potential energy are relevant to competitive exams. The most common ones include gravitational potential energy and elastic potential energy. In electromagnetism, electric potential energy is also a key concept.

Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. Near the Earth's surface, where the gravitational field is approximately uniform, GPE is given by the formula: PE = mgh, where 'm' is mass, 'g' is acceleration due to gravity, and 'h' is the height above a reference point.

Elastic potential energy (EPE) is the energy stored in a deformable object, such as a spring, when it is stretched or compressed. For an ideal spring obeying Hooke's Law, the EPE is given by: PE = ½kx², where 'k' is the spring constant and 'x' is the displacement from the equilibrium position.

Electric potential energy is the energy a charge possesses due to its position in an electric field. It is related to the work done by the electric force to move a charge from one point to another. The change in electric potential energy when a charge 'q' moves through a potential difference 'ΔV' is given by ΔPE = qΔV.

A cornerstone of physics is the principle of conservation of mechanical energy. In a system where only conservative forces do work, the total mechanical energy (the sum of kinetic energy and potential energy) remains constant. This means that potential energy can be converted into kinetic energy, and vice versa, without loss.

When solving problems involving potential energy, it's crucial to:

1. Identify the type of potential energy involved (gravitational, elastic, electric).
2. Choose a suitable reference point for zero potential energy. This choice is arbitrary but must be consistent throughout the problem.
3. Apply the relevant formula for potential energy.
4. Use the conservation of mechanical energy principle if only conservative forces are acting.
5. Consider work done by non-conservative forces (like friction or air resistance) if they are present, as they will change the total mechanical energy.