Glossary
Conservation of Energy
A fundamental principle stating that in a closed system, the total energy (sum of kinetic and potential energy) remains constant.
Example:
If a charged particle is released from rest in an electric field, its initial electric potential energy will be converted into kinetic energy as it moves, demonstrating the conservation of energy.
Coulomb's Constant (k)
A fundamental proportionality constant in electrostatics, approximately $8.99 imes 10^9 \frac{ ext{N} \cdot ext{m}^2}{ ext{C}^2}$, used in calculations involving electric force and potential energy.
Example:
In the formula for electric potential energy, Coulomb's constant () ensures the units work out and provides the correct magnitude for the interaction.
Electric Potential (Voltage)
Electric potential energy per unit charge ($V = U/q$), representing the potential energy that a unit positive charge would have at a given point in an electric field.
Example:
A 12V battery means that each Coulomb of charge passing through it gains 12 Joules of electric potential energy, illustrating the concept of voltage.
Electric Potential Energy
Energy stored in a system of charged particles due to their electric field interactions and relative positions.
Example:
When you push two positive charges closer together, you increase their electric potential energy because they repel each other.
Inverse Relationship (for U_E)
Electric potential energy between two point charges is inversely proportional to the distance between them, meaning energy decreases as the distance increases.
Example:
If you double the distance between two like charges, their electric potential energy will be halved due to this inverse relationship.
Multiple-Charge Systems (Superposition Principle)
To find the total electric potential energy in a system with more than two charges, calculate the potential energy for every unique pair of charges and sum them algebraically.
Example:
For three charges forming a triangle, you would calculate the electric potential energy for the (1,2) pair, (1,3) pair, and (2,3) pair, then add them up to find the total for the multiple-charge system.
Scalar Nature (of U_E)
Electric potential energy is a scalar quantity, meaning it has magnitude but no direction, allowing for direct algebraic summation without considering components.
Example:
When adding the potential energies of multiple charge pairs, you simply sum the values directly because of the scalar nature of electric potential energy, without needing to consider vectors.
Sign Matters (for U_E)
The sign of electric potential energy indicates the nature of the interaction: positive $U_E$ for repulsive forces (like charges) and negative $U_E$ for attractive forces (opposite charges).
Example:
A system of a positive and a negative charge will have a negative electric potential energy, indicating they are attracted to each other, illustrating how sign matters.
Two-Charge Systems (Formula)
The method for calculating electric potential energy ($U_E$) between two point charges using the formula $U_E = k \frac{q_1 q_2}{r}$.
Example:
To find the electric potential energy between an electron and a proton, you'd use the formula , plugging in their charges and separation distance.
Work-Energy Connection
The work done by an external force to arrange charges into a specific configuration is equal to the electric potential energy stored in that system.
Example:
Lifting a book against gravity does work, which is stored as gravitational potential energy; similarly, moving charges against their electric forces stores electric potential energy.
Work-Energy Theorem
A principle stating that the net work done on an object equals its change in kinetic energy, and is also related to the change in potential energy by the electric force.
Example:
If an electron accelerates in an electric field, the work done by the electric force equals the decrease in its electric potential energy and the increase in its kinetic energy, as per the Work-Energy Theorem.