Otis Singleton
A uniform electric field is one in which the electric field is constant at every point. It can be created by placing two conducting plates parallel to each other and maintaining a voltage (or potential difference) between them. The electric field is defined as a vector field that associates to each point in space the force per unit of charge exerted on an infinitesimal test charge at rest at that point. The electric field is said to point in the direction of decreasing potential, and the magnitude of the electric field equals the rate of decrease of potential with distance. If the electric potential at a point is zero, then the magnitude of the electric field at that point is also zero.
| Characteristics | Values |
|---|---|
| Definition | A uniform electric field is a physical field that surrounds electrically charged particles such as electrons. |
| Direction | Constant in direction |
| Magnitude | Constant in magnitude |
| Force | The force experienced by a particle with charge q placed in a uniform electric field E is F. |
| Work | When a particle with charge q moves from point A to point B, the environment (the electric field) does work on the particle. |
| Relationship between voltage and energy | A uniform electric field (\mathbf) is produced by placing a potential difference (or voltage) (\Delta V) across two parallel metal plates, labeled A and B. |
| Relationship between voltage and electric field | The general relationship between voltage and electric field is given by the equation: [E=-\frac{\Delta V}{\Delta s}], where (\Delta s) is the distance over which the change in potential, (\Delta V), takes place. |
| Relationship between (\Delta V) and (\mathbf) | The relationship between (\Delta V) and (\mathbf) is revealed by calculating the work done by the force in moving a charge from point A to point B. |
| Uniform charge distribution | Spherical conductors exhibit a uniform charge distribution on the surface and hence have the same electric field as that of uniform spherical surface distribution. |
| Electric field lines | Electric field lines point from positive to negative charges. |
| Radial field | A radial field emanates uniformly from a charge in all directions, as observed in the field around a point charge or a sphere. |
| Electric field strength | The magnitude of the electric field strength in a uniform field between two charged parallel plates is defined as the ratio of the potential difference and separation of the plates. |
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What You'll Learn
- Electric field lines point from positive to negative charges
- The electric field is defined as a vector field
- The relationship between \(\Delta V\) and \(\mathbf{E}\) is revealed by calculating the work done by force
- A uniform field is one in which the electric field is constant at every point
- The electric field between two parallel plates is uniform
Electric field lines point from positive to negative charges
The direction of the electric field changes as the position changes. The field always points to the left at the location exactly halfway between the two charges, as the y-components of the fields cancel each other out. As the location gets closer to the negative charge, the direction of the field is dominated by the negative charge since its magnitude is greater. Thus, the field lines curve toward the negative charges and away from the positive ones.
The magnitude of the electric field vector is represented by E, and it has both magnitude and direction. The relationship between the potential difference (or voltage) and E can be used to describe any charge distribution. The voltage between points A and B is:
> V_AB=Ed
> E=V_AB/d
Where d is the distance from A to B. The general relationship between voltage and electric field is:
> E=-ΔV/Δs
Where Δs is the distance over which the change in potential, ΔV, takes place. The minus sign tells us that E points in the direction of decreasing potential.
The electric field is a vector field, and it has a fixed magnitude for a given radial distance away from the charge. As the radius away from the source charge increases, the magnitude of the electric field decreases. This results in spherical shells of vectors pointing away from the centre in three-dimensional space.
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The electric field is defined as a vector field
The concept of an electric field extending into the space surrounding charges was first proposed by Michael Faraday. The idea that a charge interacts with the electric field surrounding the other charges in the system is a useful tool for visualising electrostatic forces. The electric field at a point may be defined as the electrostatic force that would act on a test charge placed at that point, divided by the charge of the test charge. Since the force is a vector, the electric field is also a vector. Electrostatic forces are additive and add vectorially, and since the test charge q is common to all terms in the summation, it can be divided out, showing that the electric field is additive in the same way as electric force.
The electric field is a vector field, so we can "draw a map" of the vectors around a source charge. The electric field has a fixed magnitude for a given radial distance away from the charge, with vectors pointing away from a positive source. As the radius away from the source charge increases, the magnitude of the electric field decreases. Thus, in three-dimensional space, there are spherical shells of vectors pointing away from the centre. Although a field map is difficult to depict in 3D, we can still represent it well by depicting the electric field in two dimensions.
In general, the electric field cannot be described independently of the magnetic field. The equations of electromagnetism are best described in a continuous description. However, charges are sometimes best described as discrete points; for example, some models may describe electrons as point sources where charge density is infinite on an infinitesimal section of space.
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The relationship between \(\Delta V\) and \(\mathbf{E}\) is revealed by calculating the work done by force
In a uniform electric field, the relationship between \(\Delta V\) and \(\mathbf{E}\) is revealed by calculating the work done by the force in moving a charge from one point to another. This is a complex process for arbitrary charge distributions, requiring calculus. Hence, a uniform electric field is considered a special case.
A uniform electric field \(\mathbf{E}\) is produced by placing a potential difference (or voltage) \(\Delta V\) across two parallel metal plates, labelled A and B. The electric field strength between the plates can be calculated using the formula:
$$\mathbf{E} = \frac{V_{\text{AB}}}{d}$$
Where \(V_{\text{AB}}\) is the voltage across the plates, and \(d\) is the distance between them.
The force on a charge in an electric field can be calculated using the formula:
$$\mathbf{F} = q\mathbf{E}$$
Where \(q\) is the charge. In a uniform electric field, the force on the charge is the same regardless of its location between the plates. This is because the electric field is uniform, pointing in the direction of decreasing potential.
The relationship between \(\Delta V\) and \(\mathbf{E}\) can also be expressed as:
$$\mathbf{E} = -\frac{\Delta V}{\Delta s}$$
Where \(\Delta s\) is the distance over which the change in potential, \(\Delta V\), occurs. This equation shows that the electric field is the gradient of the electric potential.
In summary, the relationship between \(\Delta V\) and \(\mathbf{E}\) is revealed by calculating the work done by the force in moving a charge between two points in a uniform electric field. This involves considering the voltage, electric field strength, and the distance between the plates, as well as understanding the direction of the force and the concept of decreasing potential.
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A uniform field is one in which the electric field is constant at every point
The electric field is defined as a vector field that associates to each point in space the force per unit of charge exerted on an infinitesimal test charge at rest at that point. The SI unit for the electric field is the volt per meter (V/m), which is equal to the newton per coulomb (N/C). The electric field acts between two charges, just as the gravitational field acts between two masses, and it can be visualised using 'lines of force', a concept introduced by Michael Faraday. These field lines always originate from positive charges and terminate at negative charges.
The electric field between two charged parallel plates is uniform, with equally spaced field lines directed from the positive to the negative plate. The field strength between the plates is the ratio of the potential difference and separation of the plates. This can be calculated using the equation E=V/d, where E is the electric field strength, V is the potential difference, and d is the distance between the plates.
The relationship between the potential difference and the electric field can be revealed by calculating the work done by the force in moving a charge from one plate to another. This is more complex for arbitrary charge distributions, so a uniform electric field is often used as a special case.
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The electric field between two parallel plates is uniform
A uniform electric field is one in which the electric field strength is the same at all points. This can be created by placing two oppositely charged plates parallel to each other, resulting in a potential difference between them. The electric field between these parallel plates is uniform and can be represented by equally spaced, parallel field lines. These field lines are perpendicular to the plates, pointing from the positively charged plate to the negatively charged plate.
The electric field strength between the plates is determined by the ratio of the potential difference and the separation of the plates. This strength remains constant, meaning a charge would experience the same force regardless of its position within the field. This is analogous to a particle with mass entering a uniform gravitational field near the Earth's surface, where the gravitational force remains relatively unchanged at different points.
The presence of an electric charge creates an alteration in space known as an electric field. In the context of two parallel plates, the electric force between the source charge and a test charge is mediated by the uniform electric field. The field is a vector, meaning it points away from positive charges and toward negative charges.
The behaviour of an electron entering the uniform electric field between the plates can be calculated using specific equations. The time taken for the electron to cross the field, the upward component of its velocity, and the angle of deviation from its initial path can all be determined mathematically.
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Frequently asked questions
A uniform electric field is one in which the electric field is constant at every point. It can be produced by placing a potential difference (voltage) across two parallel metal plates. The electric field between the plates is uniform, with equally spaced field lines directed from the positive to the negative plate.
A uniform electric field is created by maintaining a voltage (potential difference) between two conducting plates that are placed parallel to each other. The electric field strength between the plates depends on the potential difference and the separation between the plates.
The relationship between voltage (\(\Delta V\)) and electric field (\(E\)) in a uniform electric field is given by the equation \(E = -\Delta V / \Delta s\), where \(\Delta s\) is the distance over which the change in potential occurs. This equation shows that the electric field points in the direction of decreasing potential.
The electric field between two parallel plates is uniform and directed from the positive plate to the negative plate. In contrast, the electric field around a point charge is non-uniform and radial, extending outward from a positive charge and converging toward a negative charge.
In a uniform electric field, the influence of the environment on a charged particle is represented by the electric field, which acts on the particle's charge, resulting in a force on the particle. This force causes the particle to experience a change in energy as it moves through the field.
