Wiktor Wise
Electric potential, also known as voltage, is a fundamental concept in physics that deals with the potential energy per unit charge in an electric circuit or system. It is crucial to understand how electric potential changes as charges move within a circuit or interact with other charges. This change in electric potential, often referred to as the potential difference, is calculated by considering the initial and final voltages and the amount of charge moved. The change in potential energy, denoted as ΔPE, plays a significant role in understanding the behaviour of charges within electrical systems and is defined as the change in potential energy of a charge moved from one point to another, divided by the charge. This concept is essential for comprehending the energy transformations and interactions that occur in various electrical devices and circuits.
| Characteristics | Values |
|---|---|
| Definition | Electric potential V is the potential energy per unit charge. |
| Formula | The change in potential energy is defined as the change in potential energy of a charge q moved from point A to point B, divided by the charge. |
| Units | The units of electric potential are joules per coulomb, or volts (V). |
| Voltage | Voltage is the common name for electric potential difference. |
| Reference Level | The reference level for electric potential is infinity, where the force on a test charge is zero. |
| Electrostatic Potential | The electrostatic potential between two charges q1 and q2 separated by a distance r is given by Coulomb's law. |
| Energy Output | To find the energy output, multiply the charge moved by the potential difference. |
| Conservative Force | The electrostatic or Coulomb force is conservative, meaning the work done on q is independent of the path taken. |
| Work Done | The work done by a conservative force is equal to the negative of the change in potential energy (Work = – ΔPE). |
| Battery Terminals | The positive terminal of a battery is at a higher voltage than the negative terminal. |
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What You'll Learn
Electric potential energy per unit charge
Voltage, or electric potential difference, is the difference in electric potential energy per unit charge between two points in a circuit. It is important to consider voltage as a relative value, always referring to two distinct points, as it is meaningless to discuss the voltage at a single point in isolation. The voltage between points A and B represents the disparity in the amount of potential energy per unit charge at those locations.
The concept of electric potential energy per unit charge is closely tied to the idea of potential energy in conservative Coulomb fields. In electrostatics, it is essential to differentiate between potential, potential difference, and potential energy. Electric potential energy refers to the energy expended in assembling a system of charges, bringing them together from an infinite distance. On the other hand, electric potential at a point signifies the change in potential energy of the system when a unit charge is introduced to that specific point.
Mathematically, the electrostatic potential energy, UE, of a point charge q in the presence of n point charges Qi, considering an infinite separation between the charges as the reference position, can be calculated using the formula provided in the source material. This formula takes into account the distances between the charges and their assigned values. Additionally, Coulomb's law plays a significant role in understanding the relationship between electric fields, electrostatic forces, and the configuration of charges within a system.
Understanding electric potential energy per unit charge is essential in explaining various electrical phenomena, such as the flow of current in a circuit. Voltage, as a measure of potential energy per unit charge, influences the current in a circuit. A higher voltage, or electromotive force, leads to a higher current. This relationship demonstrates how the potential energy per unit charge drives the movement of charges within a circuit, similar to how gravitational potential energy affects the movement of objects in a gravitational field.
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Potential difference between two points
The potential difference between two points in a circuit, also known as voltage, is the work required per unit of charge to move a test charge between the two points. It can be understood as the change in potential energy and other forms of energy of a unit charge when it is moved from one point to another.
The SI unit of potential difference is the volt (V), and 1 volt is equal to the work done in transporting a unit positive charge of 1 coulomb from one place to another, requiring 1 joule of energy. This process can be represented by the equation:
> $ ( V_{B}-V_{A} (\Delta V) = \Delta U/q )$
Where $V_{B}$ is the potential at point B, $V_{A}$ is the potential at point A, and $\Delta V$ is the change in potential or potential difference.
To create and sustain a potential difference, charges must be moved "the wrong way", that is, towards the point of higher potential. This requires a force larger than the repelling force, which can be provided by a voltage source such as a battery.
In a battery, a chemical process creates a force that pushes electrons back up to the higher potential point (the negative pole/terminal of the battery). From this point, they want to move back to the lower potential by running through the circuit. This movement of electrons creates a potential difference between the two points in the circuit.
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The work done by a conservative force
In physics, a conservative force is a force that, when moving a particle between two points, does work independent of the path taken. In other words, the work done by a conservative force depends only on the initial and final positions of the objects involved. The most familiar conservative forces are gravity, the electric force (in a time-independent magnetic field), and spring force.
The formula for calculating the work done by a conservative force is W = Fd, where W is the work done, F is the force acting on the object, and d is the distance between the force and the object. To find the total work done by the force, you can multiply the magnitude of the force by the distance it moves, and then divide this number by the time it takes for the object to move that distance, giving you the average power output of the force.
A conservative force can be understood as a force that conserves mechanical energy. If a particle starts at point A and is moved around by other forces, eventually ending up at A again, it has traveled a closed path. If the net work done at this point is 0, then the force passes the closed path test and is classified as a conservative force.
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The potential energy of a charge
Electric potential energy is a scalar quantity with only magnitude and no direction. It is the potential energy (measured in joules) that results from conservative Coulomb forces. It is associated with the configuration of a particular set of point charges within a defined system. An object may possess electric potential energy due to its own electric charge or its relative position to other electrically charged objects.
The electric potential energy of a system of point charges is defined as the work required to assemble this system of charges by bringing them together from an infinite distance. The electric potential energy of any given charge or system of charges is the total work done by an external agent in bringing the charge or the system of charges from infinity to the present configuration without undergoing any acceleration.
The electrostatic potential energy, UE, of one point charge q at position r in the presence of an electric field E is defined as the negative of the work W done by the electrostatic force to bring it from the reference position rref to that position r. The electrostatic potential energy can also be defined from the electric potential as the electric potential generated by the charges, which is a function of position r.
The electric potential at infinity is zero. The total electric potential of the charge is defined as the total work done by an external force in bringing the charge from infinity to the given point. The electric potential energy of the system decreases if two unlike charges, such as a proton and an electron, are brought towards each other. If two like charges, such as two protons or two electrons, are brought towards each other, the potential energy of the system increases.
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Voltage and energy
The concepts of voltage, charge, current, and energy are closely linked. Current is the flow of electrical charge, with the charge carried by electrons moving around a circuit. The amount of charge that moves is dependent on the size of the current and the time it flows for. Voltage is sometimes referred to as "electrical pressure" and can be understood using the height analogy for potential energy. In this analogy, height corresponds to voltage and mass to charge.
Potential energy is the product of mass, gravity, and height. Keeping gravity constant, an object with a greater mass or higher position will have greater potential energy. This potential energy can be thought of as the object's ability to cause damage when released. Similarly, voltage is related to the potential energy of a system. The higher the voltage, the greater the potential for energy transfer or damage.
For example, static voltage may be in the thousands of volts, but the associated energy may only be a few microjoules, which is not enough to be lethal. However, the same voltage achieved with a higher charge and energy could be deadly. Voltage is also related to the energy transferred per unit of charge passed. The equation for voltage is: Voltage (V) = Energy (J) / Charge (C).
The relationship between voltage and energy is important in understanding electrical systems. Increasing the voltage in a circuit will also increase the current, impacting the energy transfer within the system.
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Frequently asked questions
Electric potential, or potential, is the potential energy per unit charge. It is a physical quantity that is independent of test charge.
Electric potential is calculated by dividing the potential energy by the quantity of charge. The potential difference between two points, A and B, is defined as the change in potential energy of a charge q moved from A to B, divided by the charge.
Batteries repel electrons from their negative terminals and attract them to their positive terminals. The positive terminal is at a higher voltage than the negative terminal. As a battery is discharged, its terminal voltage drops.
