The concept of electric potential energy is fundamental to numerous technologies and devices. For instance, in capacitors, electric potential energy is stored and used in electronic circuits for various purposes like smoothing out electrical signals or storing charge for later use. In batteries, chemical reactions create differences in electric potential, which is then used as electric potential energy for powering devices. Photovoltaic cells (solar panels) convert light energy into electric potential energy. Even in the medical field, defibrillators use stored electric potential energy to deliver a controlled electric shock to the heart, correcting arrhythmias.

Electric potential energy can indeed be negative, and this signifies an attractive interaction between the charges. In the formula U = (k * q1 * q2) / r, if q1 and q2 have opposite signs (one positive and one negative), the product q1 * q2 becomes negative, leading to a negative value of U. A negative potential energy indicates that work must be done against the electric field to separate the charges further. In essence, the charges naturally attract each other, and energy is released when they move closer, which is characteristic of a stable, lower-energy configuration.

Understanding electric potential energy is crucial for mastering electromagnetism because it forms the basis for comprehending how charges interact in an electric field. This knowledge is foundational in analysing and predicting the behaviour of charges and currents in various electromagnetic scenarios. For instance, it aids in understanding the forces acting in electric and magnetic fields, the principles of electromotive force in circuits, and the energy transformations in electromagnetic systems. Proficiency in electric potential energy concepts also paves the way for exploring more advanced topics in electromagnetism, such as electromagnetic induction and Maxwell's equations.

If one of the charges in a two-charge system is doubled, the electric potential energy of the system also doubles. The potential energy is directly proportional to the product of the magnitudes of the two charges, as given by U = (k * q1 * q2) / r. By doubling one charge, say q1 becomes 2q1, the formula becomes U = (k * 2q1 * q2) / r, which is essentially 2 times the original potential energy. This increase reflects the enhanced electrostatic interaction due to the increased charge, leading to a higher energy state in the system.

When the distance between two charges is halved, the electric potential energy of the system changes significantly. The electric potential energy is inversely proportional to the distance between the charges, as described by the formula U = (k * q1 * q2) / r. Therefore, if the distance (r) is halved, the potential energy becomes double its original value if the charges are like, or twice as negative if the charges are unlike. This is because reducing the distance between charges increases the intensity of the electrostatic force, thus amplifying the potential energy stored within the system.