7.2 Electric Potential and Potential Difference
4 min read•june 24, 2024
and are key concepts in understanding how charges interact in electric fields. They help us quantify the energy associated with charge positions and movements, laying the groundwork for analyzing electric circuits and systems.
, measured in volts, represents the potential difference between two points. This concept is crucial for understanding energy transfer in electrical systems and forms the basis for many practical applications, from batteries to power grids.
Electric Potential and Potential Difference
Electric potential and voltage
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- represents per unit charge at a point in an electric field measured in joules per (J/C) or volts (V), denoted by the symbol
- another term for potential difference, the difference in electric potential between two points measured in volts (V), denoted by the symbol
- Potential difference the change in electric potential energy per unit charge when a charge moves between two points in an electric field, mathematically expressed as , where is the change in potential energy and is the charge
- Example: A 5 V battery maintains a potential difference of 5 V between its terminals
- Example: An electron moving through a potential difference of 10 V gains 10 eV of energy
Calculations of potential difference
- Electric potential at a point due to a point charge calculated using the formula
- ###'s_Constant_0### ()
- the point charge creating the electric field
- the distance from the point charge to the point of interest
- Potential difference between two points calculated using the done by the electric field:
- the electric field vector
- the displacement vector between the two points
- For a uniform electric field, the potential difference simplifies to , where is the distance between the points
- Example: Two parallel plates separated by 1 cm with a uniform electric field of 1000 V/m between them have a potential difference of 10 V
- The potential difference is path-independent, meaning the done by the electric field depends only on the initial and final positions, not the path taken between them
Electron-volt as energy unit
- (eV) a unit of energy equal to the work done on an electron when it moves through a potential difference of one ,
- Electron-volts commonly used in atomic and nuclear physics to express energies of particles and transitions
- Ionization energies and binding energies of electrons in atoms often given in eV (hydrogen atom's ground state: -13.6 eV)
- Nuclear reaction energies and particle energies in particle physics expressed in eV or its multiples (keV, MeV, GeV) (proton rest mass energy: 938 MeV)
Energy conservation in electric systems
- In , the total energy (kinetic + potential) of a charged particle remains constant:
- and the particle's velocities at points 1 and 2
- and the electric potentials at those points
- This principle used to solve problems involving the motion of charged particles in electric fields
- Example: Determining the speed of an electron accelerated through a potential difference (electron accelerated from rest through 100 V reaches a speed of m/s)
- Example: Calculating the maximum height reached by a charged particle in a uniform electric field (proton launched vertically in a 1000 V/m field with an initial speed of m/s reaches a maximum height of 51.1 m)
Equipotential lines and surfaces
- or surfaces regions in an electric field where all points have the same electric potential, no work done when a charge moves along an equipotential line or surface
- Equipotential lines always perpendicular to electric field lines, the direction of the electric field at any point given by the of the electric potential
- Spacing between equipotential lines indicates the strength of the electric field
- Closely spaced equipotential lines represent a strong electric field
- Widely spaced equipotential lines represent a weak electric field
- Analyzing the shape and spacing of equipotential lines helps visualize the behavior of electric fields in various configurations
- Example: Parallel plates have evenly spaced, parallel equipotential lines, indicating a uniform electric field
- Example: Point charges have circular equipotential lines, with spacing increasing as distance from the charge increases (electric field strength decreases with distance)
- Example: An has more complex equipotential lines, reflecting the combined effect of two opposite charges
Electrostatic potential energy, work, and capacitance
- is the energy stored in a system of charges due to their relative positions
- Work done by an electric field is related to the change in electrostatic potential energy and the potential difference
- is a measure of a system's ability to store electric charge, defined as the ratio of charge to potential difference
Key Terms to Review (33)
Ac voltage: AC voltage is a type of electrical current where the voltage periodically changes direction. It is commonly used in household power supplies and electrical grids due to its efficiency in long-distance transmission.
Binding Energy: Binding energy is the energy required to separate a system into its individual components. In the context of electric potential and potential difference, binding energy refers to the work needed to move charges against electric forces, ultimately defining how much energy is stored in a charged system and how it behaves under influence from external electric fields.
Capacitance: Capacitance is the ability of a system to store charge per unit voltage. It is measured in farads (F).
Capacitance: Capacitance is a measure of the ability of a capacitor to store electric charge. It is a fundamental quantity in the study of electricity and electronics, and it plays a crucial role in various topics related to electrostatic equilibrium, electric potential, and energy storage.
Conservative Electric Fields: A conservative electric field is a type of electric field where the work done in moving a charge between two points is independent of the path taken. This means the work done is solely determined by the initial and final positions of the charge, and not the specific trajectory it follows.
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.
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 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).
Electron-volt: An electron-volt (eV) is a unit of energy equal to approximately $1.602 \times 10^{-19}$ joules. It is the amount of kinetic energy gained or lost by an electron when it moves through an electric potential difference of one volt.
Electron-Volt: The electron-volt (eV) is a unit of energy commonly used in physics to measure the energy gained or lost by a single electron when it is accelerated through an electric potential difference of one volt. It is a fundamental unit that connects the concepts of electric potential and energy.
Electrostatic Potential Energy: Electrostatic potential energy is the potential energy possessed by an electric charge due to its position within an electric field. It is the work done by an external force in bringing a charge from infinity to a specific location in the electric field.
Equipotential Lines: Equipotential lines are imaginary lines in an electric field that connect points with the same electric potential. These lines represent the spatial distribution of electric potential and provide a visual representation of the electric field.
Equipotential surfaces: Equipotential surfaces are hypothetical surfaces where the electric potential is constant throughout. This means that any point on a given equipotential surface has the same electric potential energy per unit charge, which implies that no work is done when moving a charge along this surface. Understanding equipotential surfaces helps clarify how electric fields interact with charged objects and their distributions.
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.
Ionization Energy: Ionization energy is the minimum amount of energy required to remove an electron from an atom or molecule, forming a positively charged ion. It is a fundamental property that describes the strength of the attractive force between an electron and the nucleus of an atom.
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.
Kinetic Energy: Kinetic energy is the energy of motion possessed by an object due to its movement. It is the energy that an object has by virtue of being in motion and is directly proportional to the mass of the object and the square of its velocity.
Path independence: Path independence refers to the concept that the work done by a force on an object moving from one point to another does not depend on the specific path taken, but only on the initial and final positions. This principle is crucial in understanding electric potential and potential difference, as it implies that electric potential energy changes are determined solely by the locations in an electric field rather than the route taken between them.
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.
Potential Energy: Potential energy is the stored energy in an object due to its position or configuration in a force field, such as gravitational or electric fields. This form of energy can be converted into kinetic energy when the object is allowed to move or change position, playing a crucial role in various physical systems. Understanding potential energy helps explain how electric forces act between charges and the concept of voltage in electric circuits.
Spark chamber: A spark chamber is a particle detector used to visualize the passage of charged particles through a medium. It operates by detecting ionization trails left by particles as they pass through an inert gas between parallel plates.
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.
Volt (V): A volt (V) is the derived unit for electric potential, electric potential difference, and electromotive force in the International System of Units (SI). One volt is defined as the potential difference that will move one coulomb of charge with an energy of one joule.
Voltage: Voltage, also known as electric potential difference, is the measure of potential energy per unit charge between two points in an electric field. It is measured in volts (V).
Voltage: Voltage, also known as electrical potential difference, is the driving force that causes the flow of electric current in a circuit. It is the measure of the potential energy difference between two points in an electrical system, and it is the key factor that determines the rate at which electric charge moves through a conductor.
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.