Beatrice Lang
Voltage and electric force are fundamental concepts in physics that are closely related. Voltage, often referred to as electric potential, is a measure of the potential for an electrical charge to perform work. It is quantified in joules per coulomb of electric charge. Electric force, on the other hand, is the force exerted per unit charge and is measured in newtons per coulomb. The relationship between voltage and electric force is intricate and can be understood through the lens of electric fields and the movement of charged particles. Electric fields, which are present around electric charges, create forces that influence the behaviour of charged particles. The interplay between electric fields, voltage, and electric force is essential for comprehending the dynamics of electrical systems.
| Characteristics | Values |
|---|---|
| Voltage | Electrical energy per unit charge |
| Electric field | Force per unit charge |
| Voltage and electric field strength | Directly related |
| Voltage | Work done per unit charge in an electric field |
| Electric field strength | Measure of the intensity of an electric field at a particular location |
| Electric field strength | Defined as the force experienced by a unit positive charge placed at a point |
| Electric field strength | Measured in newtons per coulomb (N/C) or volts per metre (V/m) |
| Relationship between voltage and electric field strength | For a given distance, the voltage increases with increasing electric field strength |
| Uniform electric field | Voltage is evenly distributed across the field |
| Non-uniform electric field | Voltage varies across the field, resulting in different electric field strengths at different points |
| Electric field strength | The force produced by a charge q and experienced by a +1 C charge |
| Voltage | Potential energy of the system |
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What You'll Learn
Electric field strength and voltage
Electric field strength, on the other hand, is a measure of the intensity of an electric field at a particular location. It is defined as the force experienced by a unit positive charge placed at that point. The electric field is generated by a charge and can be thought of as the force that would be experienced by a small, stationary, positively charged object at a particular point in space. The electric field strength decreases as the distance from the charge increases.
The relationship between voltage and electric field strength can be expressed mathematically as V = Ed, where V is voltage, E is electric field strength, and d is the distance over which the charge moves. This equation demonstrates that voltage increases with increasing electric field strength for a given distance. Conversely, for a fixed electric field strength, voltage decreases as the distance increases.
In a uniform electric field, the voltage is evenly distributed, resulting in the same electric field strength at all points. However, in a non-uniform field, the voltage varies, leading to different electric field strengths at different points.
Understanding the relationship between electric field strength and voltage is essential for comprehending various aspects of electric circuits and electric field theory.
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Electric potential difference
Voltage is often referred to as electric potential or potential difference. It is measured in volts (V) in the International System of Units (SI). The volt is a derived unit, and one volt is equal to one joule of energy per coulomb of charge (1 V = 1 J/C). This relationship highlights that voltage is not the same as energy but rather represents the energy per unit charge.
To understand voltage, consider a simple analogy with a water circuit. Imagine a closed-loop of pipework with water flowing through it, driven by a mechanical pump. The potential difference in this system corresponds to the pressure difference between two points. If the pump creates a pressure difference, it enables water to flow and perform work, such as driving a turbine. Similarly, in an electrical circuit, the voltage provided by a battery creates a potential difference, allowing electric charges to move and perform work, like turning an automobile's starter motor.
The concept of electric potential difference is closely related to electric fields. An electric field is present near any electric charge and exerts a force on other charges within its vicinity. The electric field strength is measured in Newtons per Coulomb (N/C), representing the force per unit charge. When an electric field is constant, the electric potential difference can be calculated based on the change in potential with distance.
The relationship between electric potential difference and particle charges is often expressed using the unit electron-volt (eV). For example, a potential difference of 100,000 volts (100 kV) gives an electron an energy of 100,000 electron-volts (100 keV). This simple relationship between voltage and particle charge is commonly used in submicroscopic processes, such as describing chemical valence energies or nuclear binding energies.
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Electric force and voltage in a gravitational analogy
Electric force and voltage can be understood through a gravitational analogy. Voltage is often referred to as potential, as it measures the potential for an electrical charge to do work. This is similar to how height is related to gravitational energy in a gravitational analogy, where height represents voltage.
In a gravitational system, an object possesses gravitational potential energy, measured in Joules, when placed at a certain point in space. This potential energy is determined by the object's height, mass, and the strength of the gravitational field. Similarly, in an electrical system, voltage is the difference in electric potential between two points, measured in Joules per Coulomb of electrical charge. A Coulomb placed on the positive side of a battery can perform a greater amount of work compared to one on the negative side, and this difference in potential energy is the voltage.
Using the analogy of a topographical map, we can visualise the relationship between field and voltage. Each contour line represents a constant height, similar to how constant-voltage curves surround a point charge. Where the contour lines are close together, the slope is steep, indicating a strong electric field. This is analogous to a steep hillside, where the altitude changes rapidly, representing a rapid change in voltage.
The mathematical relationship between voltage and field can be expressed as $dU = -F_xdx$ for a particle moving in one dimension along the $x$-axis. In three dimensions, the relationship becomes $E_x = -\frac{dV}{dx}, E_y = -\frac{dV}{dy}$, and $E_z = -\frac{dV}{dz}$. This demonstrates how voltage and electric field are interconnected, with voltage being electrical energy per unit charge and electric field being force per unit charge.
In summary, the gravitational analogy helps us understand electric force and voltage by comparing height and voltage, gravitational potential energy and electrical potential energy, and the slope of contour lines to the strength of the electric field. This analogy provides a useful framework for comprehending the underlying principles of electric force and voltage.
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Voltage as a measure of potential energy
Voltage is often referred to as "'potential'" because it is a measure of the potential for electrical charge to do work. It is not the same as energy, but rather the potential for a charged particle to release energy by moving between two points. Voltage is a measure of electrical potential energy per unit charge. The units of voltage are Joules per Coulomb of electrical charge, which is equal to a volt.
In other words, voltage is a charge-dependent energy. If you have a positively charged particle stuck to a negatively charged particle, they would be at rest. If you pull them apart, you have invested energy into the system, and they now have a potential energy between them that will be spent coming back together. The more charges there are (more electrons) relative to another distinct point you can measure, the higher the voltage.
The relationship between voltage and electric force can be understood through the concept of electric fields. An electric field is created by a constant electric charge near an object. This electric field will exert a force on a charged particle within it, pushing it in a specific direction depending on the charge. If you want to move the particle in a different direction, you must apply an external force to counteract the force of the electric field.
The work done to move the charged particle against the force of the electric field results in a change in the electric potential energy of the system. This change in electric potential energy is what we refer to as voltage. It is important to note that voltage is not the same as potential energy but is related to it through the concept of electric potential. Electric potential refers to the potential for a charged particle to release energy, while mechanical potential refers to the potential to convert energy to another form.
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Electric field strength and voltage in a uniform vs non-uniform field
Electric field strength and voltage are closely related concepts, with voltage often referred to as potential, as it measures the potential for an electric charge to do work. This work is done on a unit of charge, with the unit of voltage being Joules per Coulomb of electrical charge.
In a uniform electric field, the field lines are depicted as parallel and equidistant, indicating a constant strength and direction of the field. The force experienced by a charged particle in a uniform field is consistent in magnitude and direction at any point within the field. The relationship between voltage, field strength, and distance in a uniform electric field is crucial for understanding electrical phenomena. The electric field strength in a uniform field can be calculated using the equation $E = \Delta V / \Delta d$, where $\Delta V$ is the voltage change and $\Delta d$ is the distance over which this change occurs. This equation demonstrates a direct relationship between voltage and electric field strength.
In contrast, a non-uniform electric field does not have constant field strength and direction. In diagrams, non-uniform fields are depicted with lines that converge, diverge, or are unevenly spaced. The effectiveness of non-uniform fields in certain applications, such as in electrocoalescence, has not been extensively studied. However, non-uniform fields are essential in some cases, such as in a corona discharge where a local dielectric breakdown of the air is required.
The distinction between uniform and non-uniform electric fields is important in understanding the behaviour of charged particles. In a uniform field, the force on a charged particle is consistent, while in a non-uniform field, the force varies depending on the particle's position and the field's strength and direction.
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Frequently asked questions
Voltage is the change in electric potential energy per unit charge. It is a measure of the potential for electrical charge to do work. The electric field is the force per unit charge. The electric field strength at a particular point is defined as the force that acts on a unit of positive charge placed at that point.
The electric field strength decreases as the distance between two charges increases. The voltage is strongest where the constant-voltage curves are closest together.
Voltage is electrical energy per unit charge. Potential energy can be converted into work. Work depends on a force and a distance that are perpendicular.
