Umair Gaines
Electric potential is defined as the line integral of the electric field between two points, and it does vary with distance. The electric field of a point charge decreases relative to the distance from the charge. The potential is constant for a small vertical displacement through the centre, resulting in a zero rate of change of the electric potential, and thus zero electric field at the centre. As the test charge moves away from the two charges, there is a net vertical component to the total electric field, so the charge will feel a vertical force. The electric potential decreases in that direction, consistent with the electric field pointing in the direction of the decreasing potential.
| Characteristics | Values |
|---|---|
| Electric potential | Defined as the line integral of the electric field between two points |
| Electric field of a point charge | Decreases with \frac{1}{r^2} where r is the distance from the charge |
| Electric potential and displacement | Constant for a small vertical displacement through the center, resulting in a zero rate of change of the electric potential, and thus zero electric field at the center |
| Electric potential and voltage | Constant along a radius, (r), around a point charge; equipotential surfaces around point charges will be spherical shells |
| Voltage and distance | For small values of r (close to the source charge), the voltage changes more rapidly (larger slope) compared to larger distances from the charge |
| Electric potential and charge | For a positive source charge, electric potential is positive and decreases with distance; for a negative source charge, electric potential is negative and increases with distance |
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What You'll Learn
- Electric potential decreases with distance from a positive charge
- Electric potential increases with distance from a negative charge
- Electric potential is defined as the line integral of the electric field between two points
- The rate of change of electric potential is zero at the centre of two charges
- Equipotential surfaces are curves where the potential is constant
Electric potential decreases with distance from a positive charge
Electric potential is defined as the line integral of the electric field between two points. Due to this, electric potential energy does indeed vary with distance. The electric field of a point charge decreases with the inverse square of the distance from the charge. This means that as the distance from a positive charge increases, the electric potential decreases.
To visualize this, imagine a unit positive charge fixed in space. Now, place a unit negative charge far enough from the positive charge so that if you move it any further, the negative charge will no longer be attracted to the positive charge. At this point, you need to hold back the negative charge to prevent it from accelerating towards the positive charge. If you let go, the negative charge will start moving slowly towards the positive charge. Over time, the potential energy of the negative charge will convert into kinetic energy.
The attractive force between the two charges causes an increase in acceleration, resulting in an increase in kinetic energy and a decrease in potential energy. This relationship between electric potential and distance holds true for both positive and negative charges. However, the specific behavior of the charges depends on their nature.
For example, consider a negative charge with twice the magnitude. When released from the same initial position, it will have a greater force acting on it due to the larger charge, resulting in a faster velocity. Consequently, it will have liberated more potential energy and turned it into kinetic energy, resulting in less potential energy at the same distance. Thus, the potential energy decreases as the charge's magnitude increases.
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Electric potential increases with distance from a negative charge
Electric potential is defined as the line integral of the electric field between two points, and it does vary with distance. The electric field of a point charge decreases with the inverse square of the distance from the charge.
When dealing with a negative charge, the potential energy increases in magnitude as the force becomes stronger, but it decreases in sign as the force becomes more attractive. This means that as the negative charge increases in strength, the attractive force between the charges increases, leading to an increase in kinetic energy and a decrease in potential energy.
To illustrate this concept, let's consider an example. Imagine we have a unit positive charge fixed in space. We introduce a unit negative charge and place it far enough from the positive charge so that if we move it any further, the negative charge will no longer be influenced by the positive charge. At this distance, we need to hold back the negative charge to prevent it from being attracted towards the positive charge. If we release the negative charge, it will start moving slowly towards the positive charge. Over time, the potential energy of the negative charge due to the presence of the positive charge will convert into kinetic energy, causing the negative charge to accelerate towards the positive charge.
In summary, while electric potential generally varies with distance, the specific behaviour depends on the nature of the charges involved. In the case of a negative charge, the potential energy increases in magnitude but decreases in sign as it transforms into kinetic energy due to the attractive force between opposite charges.
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Electric potential is defined as the line integral of the electric field between two points
Electric potential, also known as electric field potential or electrostatic potential, is defined as the line integral of the electric field between two points. This definition is based on the concept of potential energy and the work done to move a charge between two points in an electric field.
Mathematically, the electric potential at any location, r, in a system of point charges is given by the sum of the individual electric potentials due to each point charge in the system. This simplifies calculations, as the addition of potential (scalar) fields is easier than the addition of electric (vector) fields. The electric potential at a reference point, typically earth or infinity, is defined as zero units.
The electric potential between two points is closely related to the electric field. The electric field is the negative space derivative of electric potential, and its direction is determined by the potential difference. If the electric field is directed from a lower potential to a higher potential, it is considered positive. Conversely, if it is directed from a higher potential to a lower potential, it is considered negative.
The electric field and electric potential are also linked to the concept of force and energy in classical mechanics. As an object moves in the direction of a force acting on it, its potential energy decreases, and this decrease in potential energy is translated into motion or kinetic energy. Similarly, the electric potential energy of a test charge in an electric field is defined by the work done to move the charge between two points, with the motion proceeding with negligible acceleration to avoid the test charge acquiring kinetic energy.
In summary, electric potential is defined as the line integral of the electric field between two points, and this definition is fundamental to understanding the behaviour of charges and electric fields in classical mechanics.
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The rate of change of electric potential is zero at the centre of two charges
Electric potential is defined as the line integral of the electric field between two points, and it does vary with distance. The potential difference between two points is of importance, and a reference point, such as Earth, is often taken to be zero potential.
When considering the electric potential between two charges, the rate of change of electric potential is zero at the centre point. This is because the distance to each charge is equal, and the potential is constant for small vertical displacements through the centre. As a result, the electric field at the centre is also zero.
For example, consider a positive test charge moved between two identical positive source charges. When the test charge is between the two source charges, the force on it is zero. This is because the electric fields from each source charge are equal in magnitude but opposite in direction, resulting in a total electric field of zero. However, the total potential at this point is not zero but rather has equal positive contributions from each charge.
Similarly, when considering a non-uniform ring of charge, the potential on the axis of the ring is zero due to equal and opposite charges being equidistant from the point of interest.
In summary, while the rate of change of electric potential is zero at the centre of two charges, resulting in a zero electric field, the total potential at this point is not necessarily zero and can be influenced by the nature of the charges.
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Equipotential surfaces are curves where the potential is constant
Electric potential is defined as the line integral of the electric field between two points, and it does vary with distance. For instance, the electric field of a point charge decreases with an inverse square relationship to the distance from the charge.
Equipotential surfaces are an important concept in understanding electric potential. These are surfaces where all points have the same electric potential, meaning a charge will have the same potential energy at every point on the surface. In other words, an equipotential surface is a locus of points with the same potential. The work done to move a charge between two points on an equipotential surface is zero, as no work is required.
Equipotential surfaces are often represented pictorially, with black or green lines used to indicate where the electric potential is constant. These are two-dimensional representations, while equipotential surfaces are three-dimensional. In a uniform electric field, any plane normal to the field direction is an equipotential surface.
Equipotential surfaces can be used to identify regions of a strong and weak field. The spacing between equipotential surfaces indicates the strength of the electric field, with closer spacing indicating a stronger field. Equipotential surfaces are directed from high potential to low potential.
In the case of a hollow-charged spherical conductor, the potential inside is constant, and the entire volume can be considered an equipotential volume. Similarly, a conductor in a static situation can be considered an equipotential surface as there can be no voltage difference, or the charges will flow.
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Frequently asked questions
Yes, electric potential changes with distance.
For a positive source charge, the electric potential is positive and decreases with distance.
For a negative source charge, the electric potential is negative and increases with distance.
The rate of change of electric potential is higher for smaller values of r, i.e., closer to the source charge, and decreases with larger distances from the charge.
Electric potential is defined as the line integral of the electric field between two points. The electric potential decreases in the direction of the electric field, which points away from the positive charge and towards the negative charge.
