Electric potential energy describes how work arises from interactions between charges, revealing how separation, sign, and magnitude influence stored energy and later motion within electric fields.

Electric Potential Energy in Point-Charge Systems

Electric potential energy is a core idea in electrostatics because it links the interaction between charges to the work required to change their separation. In the context of the OCR specification, students must understand that electric potential energy refers to the energy associated with the positions of charges within an electric field, and that for point charges, this energy depends only on their magnitudes, their signs, and the distance between them. The specification emphasises the mathematical relationship that quantifies this interaction, allowing students to calculate stored energy and interpret the physical implications of charge configurations.

When studying energy within electric fields, it is essential to note that the potential energy concept mirrors ideas encountered in gravitational fields, though with key differences linked to charge sign. Electric potential energy may be positive or negative depending on the nature of the interacting charges. Understanding this sign behaviour enables accurate predictions about whether a system of charges will tend to repel or attract, whether work must be done to bring charges together, and whether energy is released when charges move apart.

Electric Potential Energy: Core Concept

The electric potential energy between two stationary point charges arises from the work done in assembling that configuration from infinite separation.

A test charge QQQ displaced in the electric field of a fixed charge qqq, illustrating how work done against electric forces changes the potential energy of the system and why U=0U=0U=0 is defined at infinity. Source.

Charged particles experience forces that determine whether energy must be supplied or whether energy is liberated during movement. For example:
• Like charges (both positive or both negative) require work to be done to reduce the separation, resulting in positive electric potential energy at short distances.
• Unlike charges release energy when brought together, leading to negative electric potential energy that becomes increasingly negative as separation decreases.

Equipotential contours around a positive and negative point charge (dipole), illustrating how potential changes most rapidly near the charges and reflecting how the sign and separation of charges influence electric potential energy. This image includes equipotential details, which support understanding through the relationship U=qVU=qVU=qV. Source.

This sign convention is not arbitrary; it ensures consistency between force, work, and the direction of energy transfer.

Mathematical Expression for Electric Potential Energy

The OCR specification provides a clear quantitative expression for potential energy between two point charges. This formula applies only when charges are treated as points or when spherical charge distributions can be modelled as points, and the surrounding medium is vacuum or air (where permittivity is approximately the permittivity of free space).

EQUATION
—-----------------------------------------------------------------
Electric Potential Energy (U) = (1/(4πɛ0)) · (Qq / r)
U = Electric potential energy in joules (J)
Q = Charge on one point charge in coulombs (C)
q = Charge on the second point charge in coulombs (C)
r = Separation between the charge centres in metres (m)
ɛ0 = Permittivity of free space, a constant with units of F m⁻¹
—-----------------------------------------------------------------

This expression reveals that the potential energy is inversely proportional to separation. As r decreases, the magnitude of the energy increases. Moreover, the product Qq determines whether the energy is positive or negative. The formula reinforces several key principles:
• The closer the charges, the stronger the interaction.
• Energy stored in a charge configuration depends on both magnitude and sign.
• The equation is valid only in electrostatic conditions and when fields are not distorted by surrounding materials.

Interpreting Potential Energy in Physical Situations

To use electric potential energy effectively, students must interpret what the quantity means in practical contexts. It describes the stored energy in the electric field surrounding the charges, energy that can transform into kinetic energy or work done on other systems. The concept therefore acts as a bridge between forces, fields, and motion.

Important interpretive points include:
• Positive potential energy indicates a repulsive configuration that requires input energy to maintain.
• Negative potential energy indicates an attractive configuration that spontaneously moves towards lower energy when unconstrained.
• The magnitude shows how strongly a system resists or encourages separation changes.

These interpretations mirror similar ideas in gravitational interactions but with crucial differences: gravitational potential energy is always negative because masses always attract, while electric potential energy can change sign.

Relationships with Electric Potential and Work

Electric potential energy is closely linked to electric potential, defined as work done per unit charge. Since potential energy involves the product qV, the two ideas reinforce each other and must be understood in tandem. A change in electric potential energy corresponds directly to work done by or against electric forces when moving charges within a field. Tracking such energy changes allows predictions regarding charge acceleration, system stability, and energy conversion.

Students must recognise:
• Work done on a charge equals the change in its potential energy.
• Moving a charge in the direction of the electric force reduces potential energy.
• Moving a charge against the electric force increases potential energy.
• Only differences in potential energy are physically meaningful for analysing motion.

This ensures that electric potential energy remains an essential analytical tool for understanding charge dynamics as presented in the OCR A-Level Physics course.