Umair Gaines
Electric potential, also known as voltage, is a scalar field that provides information about the energy landscape produced by an electric field. It is represented by a single number at each point in space, making it easier to graph than electric fields. Electric potential-distance graphs are used to determine the potential difference between two points, with the X-axis representing the distance from the charge and the Y-axis representing the electric potential. The area under the E-r graph between two points is equal to the potential difference. The electric potential increases as the charge increases and decreases as you move away from the charge.
| Characteristics | Values |
|---|---|
| Electric potential | Scalar field |
| Electric potential | A single number at each point in space |
| Electric potential | Dependent on the position of the object |
| Electric potential | Directly proportional to the amount of charge |
| Electric potential | Inversely proportional to the distance |
| Electric potential | Positive charge, positive potential |
| Electric potential | Negative charge, negative potential |
| Electric potential | Zero for both positive and negative charges when infinitely far away from the charge |
| Electric field strength | 1/r2 relationship |
| Electric potential vs distance graph | The x-axis shows the distance away from the charge, the y-axis shows the electric potential at a certain point |
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What You'll Learn
Electric potential is a scalar field
The electric field is a vector field that any charge will produce. A scalar field, on the other hand, is a concept that describes the energy landscape that the electric field produces. Positive charges can be thought of as hills, and negative charges as valleys in this landscape. The electric potential is like a topographic map of the space surrounding the charges in question.
The electric potential is the electric potential energy per unit charge. This value can be calculated in either a static (time-invariant) or dynamic (time-varying) electric field at a specific time, with the unit joules per coulomb (J⋅C−1) or volt (V).
In some contexts, electric potential is not a scalar but a component of a 4-vector. It is not invariant with respect to boosts. However, the potential is just one component of the four-vector, and it is a scalar under the rotation group and more generally under the Galilean Group.
The electric field can be expressed as both the scalar electric potential and the magnetic vector potential. The electric potential and the magnetic vector potential together form a four-vector, so the two kinds of potential are mixed under Lorentz transformations.
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Electric potential vs distance graphs
Electric potential is a scalar field that gives an idea of the energy landscape produced by an electric field. Positive charges are like hills and negative charges are like valleys in this landscape. The electric potential is like a topographic map of the space surrounding the charges in question.
The electric potential vs distance graph is a useful tool to understand this concept. For a single positive point charge, if we choose a path in any direction moving away from the point charge, we will get a potential vs distance graph. This graph will look similar to a y=1/x graph. This means that as we get closer to the point charge, the electric potential increases. The electric potential is zero only when 'r' is infinite, i.e., the distance from the charge is infinite.
The graph can also be understood in terms of the gradient. The gradient of the V-r graph at any point is equal to the electric field strength E at that point. The electric potential around a positive charge decreases as the distance increases, and it increases with distance around a negative charge. As 'r' increases, V against 'r' follows a 1/r relation for a positive charge and a −1/r relation for a negative charge.
The electric potential can also be visualised in 3D. A 3D topographical map can be created, where the x and y axes represent the space around the charge and the z-axis represents the electric potential. For a positive point charge, this would look like a hill, similar to the energy landscape analogy.
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The X and Y axes
The X-axis, often referred to as the horizontal axis, denotes the spatial dimension of the system. It represents the distance from the charge under consideration. This distance is typically measured from the centre or the surface of the charge and extends outward in all directions. On the X-axis, you can visualise how the electric potential varies as you move closer to or farther from the charge.
The Y-axis, or the vertical axis, represents the electric potential itself. Electric potential, often referred to as voltage, is a scalar field that provides a measure of the electric potential energy per unit of charge. In other words, it quantifies the amount of electric potential energy associated with each unit of charge in the system. The Y-axis illustrates the magnitude of this electric potential at different points in space, giving an overview of the energy landscape surrounding the charge.
The relationship between the X and Y axes is crucial. As you move along the X-axis, representing changes in distance from the charge, the corresponding electric potential on the Y-axis fluctuates. For a positive charge, the electric potential decreases as you move away from the charge, approaching zero as the distance tends to infinity. Conversely, for a negative charge, the electric potential remains negative regardless of the distance, but its magnitude decreases as you move farther from the charge. This relationship between distance and electric potential is described by the equation V = kQ/r, where V represents the electric potential, k is Coulomb's constant, Q is the charge, and r is the distance.
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Electric potential difference
> The electric potential difference between points A and B, V_B - V_A, is the change in potential energy of a charge q moved from A to B, divided by the charge.
The unit of electric potential difference is the volt (V), with 1 V equalling 1 joule per coulomb (J/C). This definition allows us to calculate the work done on a charge without considering the magnitude of the charge itself. In other words, voltage provides a convenient way to quantify the energy associated with electric charges, independent of the charge's size.
An intuitive way to visualise electric potential is through the use of an energy landscape. Positive charges can be imagined as hills, while negative charges create valleys in this landscape. The electric potential then acts as a topographic map, illustrating the spatial arrangement of charges. This representation helps us grasp the concept of electric potential difference between distinct points in space.
The concept of electric potential difference is particularly useful when dealing with batteries. For example, a car battery and a motorcycle battery might both have the same voltage of 12 volts, but the car battery can move significantly more charge, resulting in a higher energy output. This demonstrates that voltage alone does not determine the total energy available, as the amount of charge a battery can move is also a crucial factor.
In summary, electric potential difference, or voltage, is a critical concept in understanding electric charges. It allows us to quantify the energy associated with charges and facilitates comparisons between different systems, such as batteries, by providing a standardised unit of measurement—the volt.
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Electric potential energy
The electric potential is a scalar quantity, which means it only requires a single number at each point in space to characterise it. This makes it easier to work with than electric fields, which are vector fields that require both magnitude and direction. The unit of electric potential is volts, and it is often referred to as voltage.
The electric potential at a point is determined by the amount of charge present and the distance from that charge. The potential is directly proportional to the charge; as the charge increases, so does the potential, and vice versa. On the other hand, the potential is inversely proportional to the distance from the charge; as you move closer to the charge, the potential increases, and as you move away, it decreases.
To calculate the electric potential, you divide the electric potential energy by the charge. Electric potential energy is measured in joules, and the unit of charge is coulombs. The electric potential difference, or voltage, is the change in electric potential between two points. This difference can be visualised on a graph, with the x-axis representing the distance from the charge and the y-axis representing the electric potential.
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Frequently asked questions
Electric potential, also known as voltage, is a scalar field that gives you an idea of the energy landscape that the electric field produces. Think of positive charges as hills and negative charges as valleys in the energy landscape.
The X-axis of an electric potential graph shows the distance away from the charge, while the Y-axis shows the electric potential at a certain point. For a single positive point charge, the graph looks similar to a y=1/x graph. As you move away from the charge, the potential decreases and gets closer to zero.
Electric potential is calculated by dividing the potential energy by the charge. The potential is directly proportional to the amount of charge. As the charge increases, the potential increases, and as the charge decreases, the potential decreases.
The unit of electric potential is volts. Batteries typically have an electric potential of 1.5 volts, while a wall outlet is closer to 120 volts.
