Trystan Casey
Electric flux is a fundamental concept in electromagnetism that describes the total electric field passing through a given surface area in a unit of time. This is often simplified to a surface perpendicular to the flux lines. Electric flux is directly proportional to the total number of electric field lines passing through a surface. Electric flux density, denoted by the symbol D, is a way to quantify an electric field by describing the electric field in terms of flux.
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What You'll Learn
Electric flux density
An electric charge, such as a single electron in space, has an electric field surrounding it. In pictorial form, this electric field is shown as "lines of flux" being radiated from a dot (the charge). These are called Gauss lines. Field lines are a graphic illustration of field strength and direction and have no physical meaning as isolated lines. The density of these lines corresponds to the electric field strength, which could also be called the electric flux density: the number of "lines" per unit area. Electric flux is directly proportional to the total number of electric field lines going through a surface.
For a non-uniform electric field, the electric flux dΦE through a small surface area dA is given by the formula:
> dΦE = E . dA
Where E is the electric field and dA is an infinitesimal area on the surface with an outward-facing surface normal defining its direction. The electric flux over a surface is therefore given by the surface integral:
> ΦE = ∫∫ S E . dA
Where S is the surface.
The electric flux density D is related to the electric field E by the equation:
> D = ε E
Where ε is the permittivity of the medium.
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Electric field lines
Field lines are a graphic illustration of field strength and direction. The density of these lines corresponds to the electric field strength, or electric flux density, which is the number of "lines" per unit area. The number of field lines depends on the charge. The field lines never intersect each other. The field lines are perpendicular to the surface of the charge. The magnitude of the charge and the number of field lines are proportional to each other. The start point of the field lines is at the positive charge and the end point is at the negative charge.
The rules for creating an electric field diagram are as follows: Electric field lines either originate on positive charges or come in from infinity, and either terminate on negative charges or extend out to infinity. The number of lines originating or terminating at a charge is proportional to the magnitude of that charge. A charge of 2q will have twice as many lines as a charge of q.
It's important to remember that field lines are not physical entities. Although the direction and relative intensity of the electric field can be deduced from a set of field lines, they can also be misleading. For example, the field lines drawn to represent the electric field in a region must be discrete, but the actual electric field in that region exists at every point in space.
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Electric dipole
Electric flux is the total electric field that crosses a given surface. It is the total number of electric field lines passing through a given area in a unit of time. In pictorial form, an electric field is shown as "lines of flux" radiating from a dot (the charge). These are called Gauss lines. The density of these lines corresponds to the electric field strength, or electric flux density.
The "d" in electric flux refers to the infinitesimal area on the surface with an outward-facing surface normal defining its direction.
Now, an electric dipole is a specific combination of a positive charge (+Q) and an equal but opposite charge (-Q) held at a fixed distance from each other. The simplest example of this is a pair of electric charges of equal magnitude but opposite signs, separated by some distance. This distance between the two charges is also referred to as the dipole moment, which is a measure of the system's overall polarity. The SI unit for the electric dipole moment is the coulomb-metre (C⋅m). The debye (D) is another unit of measurement used in atomic physics and chemistry.
Dipoles are often found in nature, such as in water molecules, where the two hydrogen atoms are not symmetrically arranged around the oxygen atom. This results in a separation of charge, or polarization, which can be modelled as an electric dipole. When an electric dipole is immersed in a uniform electric field, the net force on the dipole is zero because the force on the positive charge is equal and opposite to the force on the negative charge. However, there is still a net torque about its centre that will cause the dipole to rotate unless the dipole vector is parallel to the electric field vector.
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Gauss's law
Electric flux is the total electric field that crosses a given surface area in a unit of time. It is measured in volt meters (V m). The total number of electric field lines passing through a given area in a unit of time defines electric flux.
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Electric flux formula
Electric flux is a property of an electric field. It can be thought of as the number of forces that intersect a given area. The concept of flux describes how much of something goes through a given area. In the case of electric flux, it is the number of electric field lines passing through a given area in a unit of time.
The mathematical relationship between the enclosed charge and electric flux is known as Gauss's Law. The SI base unit of electric flux is volt-meters (V m). The unit of electric flux is a volt-time meter. The electric flux through an area of an element is given by the formula: Φ=EAcosθ. Here, Φ (phi) is the electric flux, E is the electric field, A is the area of the surface, and θ (theta) is the angle between the electric field lines and the normal (perpendicular) to A.
For a non-uniform electric field, the electric flux is given by dΦE through a small surface area dA. The electric flux over a surface is given by the surface integral. For a closed Gaussian surface, electric flux is given by ε0, the electric constant, also called the permittivity of free space.
The electric flux through a closed surface is directly proportional to the total charge contained within that surface. The electric field E can exert a force on an electric charge at any point in space. An electric charge, such as a single electron in space, has an electric field surrounding it. In pictorial form, this electric field is shown as "lines of flux" being radiated from a dot (the charge). These are called Gauss lines.
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Frequently asked questions
Electric flux is the total electric field that crosses a given surface area in a unit of time.
In the context of electric flux, d represents an infinitesimal area on a surface with an outward-facing surface normal defining its direction. It is used in the formula for electric flux over a surface, where the electric flux is given by the surface integral.
The SI unit of electric flux is volt-meters (V m). In the CGS system, the unit of electric charge is esu, and the net flux of an electric field through a closed surface is equal to 4π times the enclosed charge.
The formula for electric flux is given by Φ = EA cos θ, where Φ is the electric flux, E is the electric field, and A is the vector area. This formula assumes that the surface is perpendicular to the flux lines for simplicity in calculations.
