Wiktor Wise
Electric potential energy, often referred to as voltage, is the energy per unit of charge at a specific point in a system. It is denoted by the letter U and measured in joules (J). When discussing the change in electric potential energy, it is common to refer to the final value minus the initial value. This is because the work done by a conservative force is the negative of the change in potential energy, i.e., W = -ΔPE. For example, when accelerating a positive charge, the work done is positive, resulting in a loss of potential energy or a negative ΔPE. This concept is crucial in understanding the behaviour of charges within an electric field and facilitates problem-solving by providing insights into energy transformations.
| Characteristics | Values |
|---|---|
| Electric potential energy | PE or U |
| Units of electric potential energy | Joules (J) |
| Work done by a conservative force | Negative of the change in potential energy; W = –ΔPE |
| Work done to accelerate a positive charge from rest | Positive and results from a loss in PE, or a negative ΔPE |
| Work done on a charge | Equal to the kinetic energy of the charge |
| Total energy of a system | Sum of kinetic and potential energy of the system |
| Conservative forces | Electrostatic force |
| Voltage | Always measured between two points |
| Electric potential | Potential energy per unit charge |
| Potential difference between points A and B | VB − VA, defined as the change in potential energy of a charge q moved from A to B |
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What You'll Learn
- Electric potential energy is denoted by PE or U and measured in joules (J)
- Work done by a conservative force is negative of the change in potential energy
- Positive work is done to increase potential energy from negative to zero
- The change in potential energy is calculated by taking one point as a reference
- Potential energy accounts for work done by a conservative force without dealing with the force directly
Electric potential energy is denoted by PE or U and measured in joules (J)
Electric potential energy is a scalar quantity with only magnitude and no direction. It is denoted by PE or U and is measured in joules (J). The SI unit of electric potential energy is the joule, named after the English physicist James Prescott Joule. The CGS system uses the erg as its unit of energy, which is equal to 10^-7 joules. Electronvolts can also be used as a unit of measurement, with 1 eV equalling 1.602 x 10^-19 joules.
The electric potential energy of an object depends on two key elements: its own electric charge and its relative position with other electrically charged objects. Electric potential energy is defined as the total potential energy a unit charge would possess if located at any point in outer space. It is the work required to assemble a system of charges by bringing them close together, or the total work done by an external agent in bringing the charge or system of charges from infinity to the present configuration without undergoing any acceleration.
The change in potential energy, ΔPE, is crucial as the work done by a conservative force is the negative of this change. For example, the work done to accelerate a positive charge from rest results from a loss in PE, or a negative ΔPE. PE can be calculated at any point by taking one point as a reference and computing the work required to move a charge to the other point.
On a macroscopic scale, the energy per electron is very small, only a tiny fraction of a joule. However, on a submicroscopic scale, this energy per particle can be significant. Even a small fraction of a joule can be enough for particles to destroy organic molecules and harm living tissue.
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Work done by a conservative force is negative of the change in potential energy
The work done by a conservative force is equal to the negative of the change in potential energy. This relationship is encapsulated in the principle of conservation of mechanical energy, which states that the total mechanical energy remains constant when only conservative forces are acting on a system.
Mechanical energy is the sum of kinetic energy (KE) and potential energy (PE) of a system, or KE + PE = constant. When dealing with conservative forces, the work-energy theorem indicates that the total mechanical energy of a system remains constant, implying that any change in potential energy results in an equal but opposite change in kinetic energy, and vice versa.
A conservative force is one for which the work done by or against it depends only on the starting and ending points of a motion and not on the path taken. Examples of conservative forces include gravitational force, spring force, and elastic force. When work is done against a conservative force to reach a final configuration, the work done is stored as potential energy, which is defined by the specific configuration of the system.
The equation W = –ΔPE illustrates the relationship between work done by a conservative force and the change in potential energy. For example, work done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative ΔPE. The minus sign in front of ΔPE is necessary to make W positive.
In summary, the work done by a conservative force is equal to the negative of the change in potential energy because conservative forces store the work done as potential energy, and any change in potential energy results in an equal but opposite change in kinetic energy.
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Positive work is done to increase potential energy from negative to zero
The concept of positive and negative work is closely tied to the change in potential energy of a system. When we do work to increase the potential energy of a system, we are effectively increasing its stored energy, which can be released or converted into other forms of energy.
In the context of electric potential, the choice of initial and final values is indeed a convention, with the final value often being subtracted from the initial value to determine the change in potential energy. This convention simplifies calculations and ensures consistency in how we understand and manipulate electric potentials in circuits and electrical systems.
Now, let's delve into the statement, "Positive work is done to increase potential energy from negative to zero." Here, the term "positive work" refers to the work done on a system, which results in an increase in the system's potential energy. In this specific case, we are considering a scenario where the initial potential energy is negative, and the goal is to raise it to zero.
Imagine lifting an object off the floor. As you lift the object, you are doing positive work, and the potential energy of the object increases. Initially, when the object is on the floor, its potential energy is considered negative because it has the potential to do work by falling to the ground due to gravity. As you lift it up, you are increasing its potential energy, taking it from a negative value to zero when it is held at a height. At this point, the object is said to have zero potential energy regarding its height, as it is not displaced from its reference position.
This scenario aligns with the concept of conservation of energy. When you do positive work by lifting the object, you are transferring energy to it, increasing its potential energy. Simultaneously, your body expends chemical energy, demonstrating that energy is conserved within the system.
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The change in potential energy is calculated by taking one point as a reference
The change in potential energy, denoted by ΔPE, is a crucial concept in understanding the work done by a conservative force. This change in potential energy can be calculated by taking one point as a reference and determining the work required to move a charge to another point. This calculation is represented by the equation W = –ΔPE, where W is the work done.
For example, consider accelerating a positive charge from rest. This results in a positive work value due to the loss in potential energy, or a negative ΔPE. To ensure that the work done, W, is positive, a minus sign must precede ΔPE in the equation. By selecting a reference point, we can compute the potential energy at any location.
In the context of gravitational potential energy, the reference point is typically chosen such that U(r) = 0 for r approaching infinity. This choice simplifies the calculation of the potential energy at a specific point. However, it's important to note that the choice of reference point does not alter the underlying physics. For instance, selecting U(a) = 0 yields a different equation, but the fundamental principles remain unchanged.
The calculation of gravitational potential energy involves multiplying the mass of an object (m) by the height above the reference level (h) and the gravitational acceleration at the reference point (g). This calculation can be expressed as E = m · g · h, with the result in joules when using SI units. For instance, consider an apple with a mass of 0.1 kg hanging at a height of 2.5 m. By multiplying these values with the gravitational acceleration (approximately 9.81 m/s² near the Earth's surface), we find the gravitational potential energy to be approximately 2.4525 J.
Understanding the change in potential energy is essential in various applications, including electron guns, where voltages higher than 100 V are commonly employed to accelerate electrons to speeds necessitating relativistic considerations. The choice of reference point for calculating potential energy can vary, but in cases where the force is constant, the choice of reference point does not impact the consistency of the potential difference result.
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Potential energy accounts for work done by a conservative force without dealing with the force directly
The work done by a conservative force is related to the change in potential energy. This is because it only depends on the initial and final positions, storing the energy as potential. Kinetic energy is accounted for separately in the work-energy theorem, which states that net work equals change in kinetic energy.
Potential energy is the energy a system has due to its position, shape, or configuration. It is stored energy that is completely recoverable. A conservative force is one for which the work done by or against it depends only on the starting and ending points of a motion and not on the path taken. We can define a potential energy (PE) for any conservative force. The work done against a conservative force to reach a final configuration depends on the configuration, not the path followed, and is the potential energy added.
For example, when you wind up a toy, an egg timer, or an old-fashioned watch, you do work against its spring and store energy in it. This stored energy is recoverable as work and is useful to think of as potential energy contained in the spring.
In a system with only conservative forces, mechanical energy is conserved, linking changes in potential energy to corresponding changes in kinetic energy. When dealing with conservative forces and ignoring other forces like friction, the work-energy theorem indicates that the total mechanical energy (the sum of kinetic and potential energy) of a system remains constant.
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Frequently asked questions
The change in potential energy, ΔPE, is crucial, as the work done by a conservative force is the negative of the change in potential energy, i.e. W = –ΔPE. Therefore, when a conservative force does negative work, the system gains potential energy, and when it does positive work, the system loses potential energy.
Voltages are always measured between two points. The potential difference between points A and B, VB − VA, is defined as the change in potential energy of a charge q moved from A to B, equal to the change in potential energy divided by the charge.
Mechanical energy is the sum of the kinetic energy and potential energy of a system, i.e. KE + PE = constant. A loss of PE of a charged particle becomes an increase in its KE.
