Wiktor Wise
Electric potential, also known as electric field potential or electrostatic potential, is a fundamental concept in physics that helps us understand electrical phenomena. It refers to the amount of work required to move a unit charge from a reference point to a specific point in a static electric field. The reference point is typically Earth or a point at infinity, where the electric potential is assumed to be zero. Electric potential is influenced by the charge of an object and its relative position to other electrically charged objects. The unit of electric potential is the volt (V), and it is expressed in the International System of Units (SI) as joules per coulomb (J/C).
| Characteristics | Values |
|---|---|
| Definition | Electric potential energy per unit of electric charge |
| Other names | Electric field potential, potential drop, electrostatic potential |
| Formula | V(vec r)=-∫ vec E.cdot dvec r + C |
| Unit | Volt (V) |
| Reference point | Typically, the reference point is Earth, or a point at infinity, although any point can be used |
| Reference level | Zero units |
| Scalar field | V(vec r) |
| Scalar potential | V |
| Scalar quantity | V or φ |
| Vector quantity | Electrostatic field |
| Work done | W = F'd = -qEd |
| Potential energy | Depends on the amount of work done in moving the object from one point to another against the electric field |
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What You'll Learn
Electric potential energy
The electric potential energy of an object is influenced by its own charge. If an object carries a charge, it will experience a force that drives it towards a position of lower electric potential energy. Positive charges will move from regions of high electric potential to low electric potential, while negative charges will move in the opposite direction, from low to high electric potential. This movement is governed by the intrinsic properties of the object, such as its mass or charge, and its position relative to other charged objects.
The electric potential energy of an object can be calculated by considering the work done to move the object from one point to another against an electric field. This work is directly related to the force acting on the object and the distance it travels. The electric potential, or voltage, is expressed in volts (V) and represents the potential energy per unit charge. The electric potential at infinity or a reference point, typically the Earth, is assumed to be zero.
The electric potential energy of a system of charges can also be determined. When two like charges, such as two protons or two electrons, are brought closer together, the potential energy of the system increases. Conversely, when two unlike charges, such as a proton and an electron, are brought together, the potential energy of the system decreases. Understanding electric potential energy helps explain the behaviour of charged particles and is essential for designing and analysing electrical circuits and systems.
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Electric potential in classical mechanics
Electric potential, also known as electric field potential, potential drop, or electrostatic potential, is a fundamental concept in classical mechanics. Classical mechanics explores concepts such as force, energy, and potential, and the interplay between them. Electric potential is defined as the electric potential energy per unit of electric charge. In other words, it is the amount of work required to move a test charge from a reference point to a specific point in a static electric field. The reference point is typically Earth or a point at infinity, where the electric potential is defined as zero.
The electric potential is influenced by the relative position of objects within an electric field. The magnitude of the electric potential depends on the amount of work done to move an object from one point to another against the electric field. When an object is moved against the electric field, it gains electric potential energy, which is defined as the total work done by an external agent to bring the charge from infinity to the given position. This energy arises due to the electric fields and Coulomb forces between charged particles.
The electric potential is closely related to the concept of potential energy. In classical mechanics, potential energy refers to the stored potential energy of a system, which depends on the relative positions of its parts. The potential energy of a system of particles is determined by the initial and final configurations of the particles and is independent of the path they travel. The electric potential energy of a charged object, specifically, is influenced by its own electric charge and its position relative to other charged objects.
The electric potential can be calculated using equations in the International System of Units (SI), expressed in joules per coulomb or volts. The equations take into account the electric field, the distance between charges, and the magnitude of the charges. By understanding the electric potential, we can gain insights into the behaviour of charged objects within electric fields and the work required to move them between different points.
Overall, electric potential plays a crucial role in classical mechanics by helping us understand the relationship between force, energy, and the positions of objects within an electric field. It provides a framework for analyzing and predicting the behaviour of charged particles and their interactions with electric fields.
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Electric potential in electrodynamics
Electric potential, also known as electric field potential, potential drop, or electrostatic potential, is a fundamental concept in electrodynamics. It is defined as the electric potential energy per unit of electric charge. In other words, it represents the amount of work required to move a test charge from a reference point to a specific point in a static electric field. The reference point is typically Earth or a point at infinity, where the electric potential is assumed to be zero.
The electric potential is a scalar quantity, often denoted by the uppercase italic letter "V" or occasionally "φ." It is related to the electric field, which is a vector field derived from force. The electric field represents the force experienced by a positive test charge at each location in space. On the other hand, electric potential is a scalar field derived from energy and represents the electric potential energy per unit charge at each location in space.
In electrodynamics, the presence of time-varying fields introduces complexity. In such cases, the electric field cannot be expressed solely as a scalar potential. Instead, it is described using both the scalar electric potential and the magnetic vector potential, which together form a four-vector under Lorentz transformations. This combination allows for a more comprehensive understanding of the electric and magnetic fields and their interactions.
The electric potential is a continuous function in all space. It is important to note that only differences in potential energy are measurable. The work done in moving a unit charge between two points in an electric circuit is equal to the difference in potential energy at those points, and this difference is measured using a voltmeter. The electric potential is influenced by the presence of charges and the relative positions of charged objects. The magnitude of the electric potential depends on the amount of work done in moving an object from one point to another against the electric field.
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Electric potential in scalar potential
Electric potential, also known as electric field potential, potential drop, or electrostatic potential, is a fundamental concept in physics. It is defined as the electric potential energy per unit of electric charge. In other words, it is the amount of work required to move a unit charge from a reference point to a specific point in a static electric field. This reference point is typically Earth or a point at infinity, and it is assumed to have zero potential.
The electric potential at any location in a system of point charges is equal to the sum of the individual electric potentials due to each point charge in the system. This simplifies calculations because adding potential (scalar) fields is easier than adding electric (vector) fields. The electric field generated by a collection of fixed charges can be expressed as the gradient of a scalar potential, which is a scalar quantity denoted by V or φ. This scalar potential is the sum of the potentials generated by each charge in isolation and can be calculated using a simple volume integral involving the charge distribution.
In mathematical physics, scalar potential describes a situation where the difference in potential energies of an object in two different positions depends only on the positions and not on the path taken by the object. It is a scalar field in three-space, meaning it is a directionless value that depends only on its location. The scalar potential is an important concept in vector analysis and physics, and it is related to the gradient of the potential energy function.
When time-varying magnetic fields are present, the electric field cannot be described solely by a scalar potential because the electric field is no longer conservative. In such cases, the electric field can be expressed as a combination of scalar electric potential and magnetic vector potential, forming a four-vector. This four-vector allows for the mixing of the two types of potential under Lorentz transformations.
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Electric potential in the International System of Units (SI)
Electric potential, also known as electric field potential, potential drop, or electrostatic potential, is defined as electric potential energy per unit of electric charge. In other words, it is the amount of work needed to move a test charge from a reference point to a specific point in a static electric field. The reference point is usually the Earth, although any point beyond the influence of the electric field charge can be used. The electric potential at the reference point is zero units.
The International System of Units, or SI units, is a universally accepted and standardized metric system for measurements. The SI unit of electric potential is volts (V) or joules per coulomb (J/C). One volt is the potential difference between two points when one joule of work is done to transfer a unit charge between them. The electric potential at infinity is assumed to be zero.
The equations used to calculate electric potential are in the forms required by SI units. In some other, less common systems of units, such as the CGS-Gaussian system, these equations would be altered. For example, in the CGS-Gaussian system, the unit of electric potential is the statvolt, which is equal to 10^-8 volts in SI units.
The electric potential at any location, r, in a system of point charges is equal to the sum of the individual electric potentials due to every point charge in the system. This simplifies calculations because the addition of potential (scalar) fields is easier than the addition of electric (vector) fields.
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Frequently asked questions
Electric potential, also known as electric field potential, potential drop, or electrostatic potential, is defined as electric potential energy per unit of electric charge.
The magnitude of electric potential depends on the amount of work done in moving an object from one point to another against an electric field.
Electric potential can be calculated using the formula V(vec r) = kQ/r, where V(vec r) is the electric potential, Q is the charge, and r is the distance from the point charge.
The unit for electric potential is the volt (V). In the International System of Units (SI), electric potential is expressed in joules per coulomb (J⋅C−1) or volts.
The reference point for electric potential is typically Earth or a point at infinity, where the electric potential is assumed to be zero. However, any point beyond the influence of the electric field charge can also be used.
