Glossary

is the stored energy in a system of charges due to their positions in an electric field. It's crucial for understanding how charges interact and move, forming the basis for concepts like voltage and electrical .

The change in energy equals the negative done by the electric field. This relationship helps us calculate energy changes as charges move, and it's essential for analyzing electric circuits and electrostatic systems.

Electric Potential Energy

Work by electric forces

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  • Work is force multiplied by in the force's direction
    • W=F⃗⋅d⃗W = \vec{F} \cdot \vec{d}
    • For electric forces, F⃗=qE⃗\vec{F} = q\vec{E}
  • In a , work equals times displacement in the field's direction
    • W=qEdcos⁡θW = qEd\cos\theta, θ\theta is the angle between electric field and displacement
    • Example: moving a charge parallel to electric field lines (θ=0°\theta = 0°) maximizes work
  • For non-constant electric fields, work is the integral of over the path
    • W=∫F⃗⋅ds⃗W = \int \vec{F} \cdot d\vec{s}
    • Example: work done moving a charge in a radial electric field depends on the path taken
  • Work done by the electric field on a charge equals the negative change in energy
    • W=−ΔUW = -\Delta U
    • Positive work by the field decreases potential energy, negative work increases it

Concept of electric potential energy

  • Electric potential energy is energy stored in a system of charges due to their positions in an electric field
  • Electric potential energy of a equals work required to assemble charges from infinite separation to their current configuration
  • Electric potential energy of qq at distance rr from point charge QQ:
    • U=kqQrU = \frac{kqQ}{r}, k=14πϵ0k = \frac{1}{4\pi\epsilon_0} (###'s_Constant_0###)
    • Example: like charges have positive potential energy, unlike charges have negative
  • Electric potential energy of a system of point charges is the sum of potential energies of all charge pairs
    • U=∑i=1n−1∑j=i+1nkqiqjrijU = \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \frac{kq_iq_j}{r_{ij}}
    • Example: potential energy of three charges is the sum of three pair-wise terms
  • Electric field is the negative of electric potential energy per unit charge
    • E⃗=−1q∇U\vec{E} = -\frac{1}{q}\nabla U
    • High potential energy regions have low electric potential, and vice versa

Changes in electric potential energy

  • Change in electric potential energy when charge qq moves from AA to BB in electric field equals negative work done by field
    • ΔU=−W=−∫ABF⃗⋅ds⃗=−∫ABqE⃗⋅ds⃗\Delta U = -W = -\int_A^B \vec{F} \cdot d\vec{s} = -\int_A^B q\vec{E} \cdot d\vec{s}
    • Example: moving a positive charge against the electric field increases potential energy
  • For point charges, change in potential energy moving charge qq from infinity to point PP:
    • ΔU=∑i=1nkqqiri\Delta U = \sum_{i=1}^{n} \frac{kqq_i}{r_i}, rir_i is distance between qq and ii-th charge qiq_i
    • Example: assembling a system of point charges from infinity
  • For continuous charge distributions, change in potential energy moving charge qq from infinity to point PP:
    1. Line charge distribution with λ\lambda: ΔU=∫kqλrdl\Delta U = \int \frac{kq\lambda}{r} dl
    2. Surface charge distribution with σ\sigma: ΔU=∫kqσrdA\Delta U = \int \frac{kq\sigma}{r} dA
    3. Volume charge distribution with ρ\rho: ΔU=∫kqρrdV\Delta U = \int \frac{kq\rho}{r} dV
  • Example: potential energy of a point charge near a uniformly charged disk or sphere
  • Electric potential is the electric potential energy per unit charge (measured in joules per )
  • is the change in electric potential between two points
  • Electromotive force (emf) is the energy per unit charge supplied by a source of electrical energy
  • surfaces are regions where the electric potential is constant

Key Terms to Review (39)

Capacitor: A capacitor is an electrical component that stores energy in the form of an electric field, created between two conductive plates separated by an insulating material. It is used to temporarily hold charge and release it when needed.
Capacitor: A capacitor is a passive electronic component that is used to store electrical energy in an electric field. It consists of two conductors separated by an insulator, and it is a fundamental component in many electrical and electronic circuits.
Charge system: A charge system refers to a configuration of charged particles that interact with each other through electric forces. Understanding this system is crucial for analyzing how electric potential energy is stored or transferred within the system, as the relative positions and magnitudes of the charges directly influence the overall energy dynamics. The charge system forms the basis for calculating electric potential energy using established formulas and concepts in electrostatics.
Constant Electric Field: A constant electric field is a region of space where the electric field strength remains the same in both magnitude and direction at all points. This means the electric field vectors have the same value and point in the same direction throughout the entire region.
Coulomb: A coulomb (C) is the SI unit of electric charge, representing the amount of charge transported by a constant current of one ampere in one second. One coulomb is equivalent to approximately $6.242 \times 10^{18}$ elementary charges.
Coulomb: The coulomb (symbol: C) is the SI unit of electric charge, named after the French physicist Charles-Augustin de Coulomb. It is a fundamental quantity that describes the amount of electric charge and is used extensively in the study of electric phenomena across various physics topics.
Coulomb's Constant: Coulomb's constant, also known as the electrostatic constant or the electric force constant, is a fundamental physical constant that describes the strength of the electrostatic force between two point charges. It is a crucial parameter in understanding and quantifying various electrical phenomena, including Coulomb's law, electric fields, electric flux, electric potential energy, and applications of electrostatics.
Dielectric breakdown: Dielectric breakdown occurs when an insulating material becomes conductive due to a high electric field, causing it to lose its dielectric properties. This results in a sudden surge of current through the material.
Dielectric Breakdown: Dielectric breakdown refers to the phenomenon where an insulating material, known as a dielectric, loses its insulating properties and becomes conductive under the influence of a strong electric field. This process can occur in various contexts, including capacitors, electric fields, and molecular structures.
Displacement: Displacement is the change in position of an object or particle relative to a reference point. It is a vector quantity, meaning it has both magnitude and direction, and is a fundamental concept in the study of physics and mechanics.
Displacement current: Displacement current is a term in Maxwell's equations that accounts for the changing electric field in regions where there is no physical movement of charge. It allows Ampère's law to be consistent with the continuity equation and is essential for explaining electromagnetic waves.
Electric dipole: An electric dipole consists of two equal and opposite charges separated by a small distance. It creates an electric field and has a dipole moment, which is a vector quantity pointing from the negative to the positive charge.
Electric Dipole: An electric dipole is a pair of equal and opposite electric charges separated by a small distance. It is a fundamental concept in electrostatics that describes the electric field and potential created by a pair of equal but opposite charges.
Electric force: Electric force is the attractive or repulsive interaction between any two charged objects. It is governed by Coulomb's Law, which states that the magnitude of the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Electric Force: Electric force is the force of attraction or repulsion between charged particles. It is the fundamental force that governs the behavior of charged objects and is described by Coulomb's law. This force is responsible for the creation of electric fields and the potential energy stored in those fields.
Electric potential: Electric potential is the amount of electric potential energy per unit charge at a specific point in an electric field. It is measured in volts (V).
Electric Potential: Electric potential, also known as electrostatic potential, is a scalar quantity that represents the amount of work done per unit charge in moving a test charge from an infinite distance to a specific point in an electric field. It is a measure of the potential energy per unit charge at a given location within an electric field.
Electric potential difference: Electric potential difference is the work done to move a unit charge between two points in an electric field. It is measured in volts (V).
Electric Potential Energy: Electric potential energy is the potential energy possessed by an electric charge due to its position in an electric field. It is the work done by an external force in moving a charge from an infinite distance to a specific location within the electric field.
Electrostatic Induction: Electrostatic induction is the process by which an electrically charged object can create an opposite charge on a nearby neutral object without making physical contact. This phenomenon arises due to the rearrangement of charges within the neutral object in response to the presence of the charged object, leading to the creation of induced charges.
Equipotential: Equipotential is a term used to describe a surface or a line in an electric field where the electric potential is constant. This means that at any point on an equipotential surface, the electric potential has the same value, and there is no potential difference between those points.
Faraday: Faraday is a fundamental concept in electromagnetism, named after the renowned British scientist Michael Faraday. It encompasses several important principles that describe the behavior of electric fields, electric potential, and the relationship between electricity and magnetism.
Gradient: A gradient is a vector that represents the rate and direction of change of a scalar field. In physics, it indicates how the electric potential changes with respect to position.
Gradient: The gradient is a vector quantity that represents the rate of change of a scalar field, such as temperature, pressure, or electric potential, in a specific direction. It indicates the direction and magnitude of the maximum rate of change of the scalar field.
Joule: The joule (J) is the fundamental unit of energy in the International System of Units (SI). It represents the amount of work done or energy expended when a force of one newton acts through a distance of one meter. The joule is a versatile unit that can be used to quantify various forms of energy, including thermal, electrical, and mechanical energy.
Linear Charge Density: Linear charge density is defined as the amount of electric charge per unit length along a charged line or distribution. It is typically represented by the symbol $$\lambda$$ and is crucial for calculating electric fields produced by charged wires or filaments, as well as for understanding how charge distributions interact with electric fields and potentials.
Non-Constant Electric Field: A non-constant electric field is a spatial distribution of electric field strength that varies with position. Unlike a constant electric field, where the field strength is uniform throughout the space, a non-constant electric field exhibits changes in magnitude and/or direction as you move from one point to another.
Point Charge: A point charge is an idealized model of an electric charge that is concentrated at a single point in space, with no physical size or dimensions. This concept simplifies the analysis of electric fields and forces, allowing for easier calculations and a clearer understanding of how electric charges interact with one another and produce electric fields.
Potential Difference: Potential difference, also known as voltage, is the measure of the work done per unit charge in moving an electric charge between two points in an electric field. It represents the potential energy difference between two locations and is a fundamental concept in the study of electric circuits and the behavior of charged particles.
Surface charge density: Surface charge density, denoted as $\sigma$, is the amount of electric charge per unit area on a surface. It is measured in coulombs per square meter ($C/m^2$).
Surface Charge Density: Surface charge density is the amount of electric charge per unit area on the surface of a charged object. It is an important concept in understanding the behavior of electric fields and electric potentials in various contexts, including charged distributions, conductors in electrostatic equilibrium, and the calculation of electric potential.
Volt: The volt is the unit of electric potential and electromotive force in the International System of Units (SI). It represents the potential difference across a conductor when a current of one ampere dissipates one watt of power. The volt is a fundamental unit that is essential in understanding and quantifying various electrical phenomena, from the storage of energy in capacitors to the generation of alternating current in household wiring.
Volta: Volta is a term that refers to the Italian physicist Alessandro Volta, who is credited with the invention of the first electric battery, known as the Voltaic pile. Volta's contributions are foundational to the understanding of electric potential energy and the calculation of electric potential, which are crucial concepts in college physics.
Voltmeter: A voltmeter is an instrument used to measure the electric potential difference, or voltage, between two points in an electric circuit. It is typically connected in parallel with the component across which the voltage is to be measured.
Voltmeter: A voltmeter is an electrical instrument used to measure the potential difference, or voltage, between two points in an electrical circuit. It is a crucial tool for understanding and analyzing electric potential energy, calculations of electric potential, and electrical measuring instruments.
Volume charge density: Volume charge density is a measure of the amount of electric charge per unit volume in a region of space. It is denoted by the symbol $\rho$ and typically expressed in units of coulombs per cubic meter (C/m^3).
Volume Charge Density: Volume charge density is a measure of the electric charge per unit volume within a given region of space. It is a fundamental concept in the study of electromagnetism and is crucial for understanding the behavior of electric fields and electric potential in various charge distributions.
Work: Work is the energy transferred to or from an object via a force acting upon it over a displacement. In physics, work is mathematically expressed as $W = F \cdot d \cdot \cos(\theta)$, where $F$ is the force, $d$ is the displacement, and $\theta$ is the angle between them.
Work: Work is a fundamental concept in physics that describes the transfer of energy due to the application of a force over a distance. It is a measure of the energy expended or transferred during a physical process and is a crucial factor in understanding the behavior of thermodynamic systems, electric potential, and the storage of energy in capacitors.
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