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Electric Flux - Definition, Formula, FAQs

Electric Flux - Definition, Formula, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 04:29 PM IST

Electric flux measures how an electric field passes through an area that was defined already. Electric flux within electromagnetism is very important because it helps in proper comprehension of how electric fields come into contact with or affect surfaces. Over the last ten years of the JEE Main exam (from 2013 to 2023), nine questions have been asked on this concept. In this article, we will discuss what is electric flux class 12, the symbol of electric flux, the electric flux formula, properties of electric flux, Gauss's law, the SI unit, the dimension of electric flux, the derivation of electric flux through a closed surface and electric flux density.

This Story also Contains
  1. What is Electric Flux Class 12?
  2. Electric Flux Formula
  3. SI Unit of Electric Flux and Dimensional Formula
  4. Properties of Electric Flux
  5. Electric Flux Density
  6. Gauss Law
  7. Derivation of Electric Flux Through a Closed Surface
  8. Solved Examples Based on Electric Flux
Electric Flux - Definition, Formula, FAQs
Electric Flux - Definition, Formula, FAQs

What is Electric Flux Class 12?

Electric flux definition: Electric flux is the rate of flow of electric lines of force across a particular area chosen as a surface.

Let us consider an electric field that is uniform in both magnitude and direction. Let these field lines penetrate a rectangular surface of area A whose plane is oriented perpendicular to the field lines. The number of electric field lines per unit area is proportional to the magnitude of the electric field. So the total number of lines penetrating is proportional to $E.A$.

The symbol of electric flux is the Greek letter phi with subscript $E$. So electric flux symbol is $\Phi_E$.

Electric Flux Formula

The magnitude of this product is known as Electric flux, which is denoted by

$\phi_E=E A$

So,

The electric flux through an area is the number of electric field lines passing normally through the area.

Electric flux through an area

The formula of electric flux through an area, dA is given by

$d \phi=\vec{E} \cdot \vec{d} A=E d A \cos \theta$

here, $\theta$ is the angle between the area vector and the electric field.

Total flux through area A is

$\phi=\int \vec{E} \cdot \vec{d} A$

SI Unit of Electric Flux and Dimensional Formula

Flux is a scalar quantity so they can be added algebraically.

The SI unit of electric flux is newton meter squared per coulomb $\left(\mathrm{N} \cdot \mathrm{m}^2 / \mathrm{C}\right)$ and volt meter $(\mathrm{V} \cdot \mathrm{m})$

Dimensional Formula

$E$ (electric field) has the dimensional formula $\left[M^1 L^1 T^{-3} I^{-1}\right]$.
$A$ (area) has the dimensional formula $\left[L^2\right]$.

Electric flux= $\mathbf{E} \cdot \mathbf{A}$

$\Phi_E=\left[M^1 L^1 T^{-3} I^{-1}\right] \times\left[L^2\right]$

thus dimension of electric flux are $\left[M^1 L^3 T^{-3} I^{-1}\right]$

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Properties of Electric Flux

  1. The electric flux is dependent on the strength of the electric field and the field passing area.
  2. The flux is maximum at an angle $\theta=0^{\circ}$ ( the field lines are perpendicular to the surface)
  3. The flux is minimum (zero) at an angle $\theta=90^{\circ}$ ( the field lines are parallel to the surface)
  4. If the field lines are pointed outwards from the surface then the electric flux is positive. If they are pointed inward to the surface, the electric flux is negative.
  5. The total flux through a closed surface with no net charge is zero.

Electric Flux Density

Electric flux density is the amount of flux passing through a unit area in an electric field. Electric flux density is also called an electric displacement field. It is given as,

$$
\mathbf{D}=\epsilon \mathbf{E}
$$

where,

Gauss Law

Gauss's law states that in a closed surface, the electric flux is directly proportional to the total charge enclosed by the surface. Mathematically it can be expressed as,

$$
\oint \mathbf{E} \cdot d \mathbf{A}=\frac{Q_{\mathrm{enc}}}{\epsilon_0}
$$

where,

  • $\oint \mathbf{E} \cdot d \mathbf{A}$ is the total electric flux through a closed surface.
  • $Q_{\mathrm{enc}}$ is the total electric charge enclosed within the surface.
  • $\epsilon_0$ is the permittivity of free space

Derivation of Electric Flux Through a Closed Surface

To understand this concept, let us take an example

Consider a cylindrical surface of radius R, length $l$, in a uniform electric field E. Compute the electric flux if the axis of the cylinder is parallel to the field direction. For this we can divide the entire surface into three parts, right and left plane faces and a curved portion of its surface. Hence, the surface integral consists of the sum of the three terms:

$\phi_E=\oint E \cdot d A=\oint_{\text {left end }} E \cdot d A+\oint_{\text {right end }} E \cdot d A+\oint_{\text {curved }} E \cdot d A$

Electric flux through a closed surface

Here, the left end and electric field are making 180o, and the right end and the electric field are making $0^{\circ}$. Also one can notice that the curved surface is making 90o with the direction of electric field. So,

$\begin{aligned}\left(\phi_E\right)_{\text {left end }} & =\oint_{\text {left end }} \vec{E} \cdot \overrightarrow{d A}=\oint_{\text {left end }} \vec{E} \overrightarrow{d A} \cos 180^{\circ}=-E \pi R^2 \\ \left(\phi_E\right)_{\text {right end }} & =\oint_{\text {right end }} \vec{E} \cdot \overrightarrow{d A}=\oint_{\text {right end }} \vec{E} \vec{A} \cos 0^{\circ}=E \pi R^2 \\ \left(\phi_E\right)_{\text {curved }} & =\oint_{\text {curved surfice }} \vec{E} \cdot \overrightarrow{d A}=\oint_{\text {curved surface }} E d A\left(\cos 90^{\circ}\right)=0 \\ \text { Total flux } & =\left(\phi_E\right)_{\text {right end }}+\left(\phi_L\right)_{\text {left end }}+\left(\phi_E\right)_{\text {curved surface }} \\ & =\left(+E \pi R^2\right)+\left(-E \pi R^2\right)+0=0\end{aligned}$

Similarly, we can find the electric flux through any closed surface by an electric field.

Also, read

Solved Examples Based on Electric Flux

Example 1: A cone of base radius $R$ and height $h$ is located in a uniform electric field $\vec{E}$ parallel to its base. The electric flux entering the cone is :
1) $\frac{1}{2} E h R$
2) $E h R$
3) $2 E h R$
4) $4 E h R$

Solution:

Electric field $\vec{E}$ through any area $\vec{A}$ -

$\begin{aligned} & \phi=\vec{E} \cdot \vec{A}=E A \cos \Theta \\ & \text { S.I unit }-(\text { volt }) m \text { or } \frac{N-m^2}{c}\end{aligned}$

wherein

Electric flux through a cone

Area of $\Delta$ facing $=\frac{1}{2} \times h \times 2 R$

$
\therefore \phi=E h R
$

Example 2: The electric field in a region of space is given by, $\vec{E}=E_0 \hat{i}+2 E_0 \hat{j}$ where $\mathrm{E}_0=100 \mathrm{~N} / \mathrm{C}$. The flux of this field through a circular surface of radius 0.02 m parallel to the Y -Z plane is nearly :
1) $0.125 \mathrm{Nm}^2 I C$
2) $0.02 \mathrm{Nm}^2 I C$
3) $0.005 \mathrm{Nm}^2 I C$
4) $3.14 \mathrm{Nm}^2 I \mathrm{C}$

Solution:

$\begin{aligned} & \vec{E}=E_0 \hat{i}+2 E_0 \hat{J} \\ & E_0=100 \mathrm{~W} / \mathrm{C} \\ & \vec{E}=100 \hat{i}+200 \hat{J} \\ & A=\pi r^2=\frac{22}{7} \times 0.02 \times 0.02 \\ & A=1.25 \times 10^{-3} \hat{i} \mathrm{~m}^2 \\ & \therefore \text { New flux } \therefore \phi=E A \cos \theta \\ & \phi=(100 \hat{i}+200 \hat{J}) .1 .25 \times 10^{-3} \hat{i} \\ & \phi=1.25 \times 10^{-1} \mathrm{Nm}^2 / \mathrm{c} \\ & =0.125 \mathrm{Nm}^2 / \mathrm{C}\end{aligned}$

Hence, the answer is the option (1).

Example 3: A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by
1) $2 \pi R^2 E$
2) $\pi R^2 / E$
3) $\left(\pi R^2-\pi R\right) / E$
4) zero

Solution:

Electric field E through any area A

$$
\begin{aligned}
& \phi=\vec{E} \cdot \vec{A}=E A \cos \Theta \\
& \text { S.I unit }-(\text { volt }) m \text { or } \frac{N-m^2}{c}
\end{aligned}
$$

wherein

electric flux through an area

Flux through surface $\mathrm{A} \quad \phi_A=E \times \pi R^2$ and $\phi_B=-E \times \pi R^2$
Flux through cursurfacesaceC $=\int E d s=\int E d s \cos 90^{\circ}=0$

Total flux through cylinder $=\phi_A+\phi_B+\phi_C=0$

Electric flux through a cylinder

Example 4: Electric field at a point varies as $r^0$ for
1) An electric dipole
2) A point charge
3) A plane infinite sheet of charge
4) A line charge of infinite length

Solution:

Electric field E through any area A

$\begin{aligned} & \phi=\vec{E} \cdot \vec{A}=E A \cos \Theta \\ & \text { S.I unit }-(\text { volt }) m \text { or } \frac{N-m^2}{c}\end{aligned}$

wherein

Electric flux through an area

$E=\frac{\sigma}{\left(2 \varepsilon_0\right)}$

Example 5: Total electric flux coming out of a unit positive charge put in air is:

1) $\varepsilon_0$
2) $\varepsilon_0^{-1}$
3) $\left(4 p \varepsilon_0\right)^{-1}$
4) $4 \pi \varepsilon_0$

Solution:

Flux may be Positive Negative or zero

For closed body.

wherein

Electric flux for closed body

$\text { Total flux coming out from unit charge }=\vec{E} d \vec{s}=1 / \varepsilon_0=\varepsilon_0^{-1}$

Frequently Asked Questions (FAQs)

1. What is flux in chemistry? Give an example of flux.

Flux is a chemical purifying agent, flowing agent or cleaning agent. Example: Ammonium chloride; Zinc chloride.

2. What is electric flux?

Electric flux, property of an electric field that may be thought of as the number of electric lines of force which intersect an area

3. What is electric flux?
Electric flux is a measure of the total electric field passing through a given surface area. It represents the flow of electric field lines through a surface and is a scalar quantity. The concept is crucial in understanding Gauss's law and electromagnetic interactions.
4. What is the unit of electric flux?

Electric flux ϕE=EAcosθ. The SI unit of electric flux is Nm2/C  

5. What are the types of Flux?
  1. Magnetic Flux.

  2. Electric flux.

  3. Luminous Flux.

  4. Radiant Flux.

  5. Heat Flux.

  6. Mass Flux.

  7. Momentum Flux.

  8. Acoustic Flux.

6. What is the electric flux direction?

The direction of an electrical field at a point is the same as the direction of the electrical force acting on a positive test charge at that point.

7. How does the angle between the electric field and the surface affect the flux?
The angle between the electric field and the surface normal affects the flux through the cosine function. When the field is perpendicular to the surface (0° or 180°), the flux is maximum. As the angle approaches 90°, the flux decreases, becoming zero when the field is parallel to the surface.
8. How does the shape of a surface affect electric flux?
The shape of a surface affects electric flux by changing the angle between the electric field and the surface normal at different points. For irregular shapes, the flux must be calculated by integrating over the entire surface, considering how the field interacts with each infinitesimal area element.
9. Can electric flux be zero even if there's an electric field present?
Yes, electric flux can be zero even in the presence of an electric field. This occurs when the electric field is parallel to the surface (θ = 90°), making cos θ = 0 in the flux equation. It can also happen if the net flux entering a closed surface equals the net flux exiting, resulting in zero total flux.
10. How does the concept of electric flux apply to a point charge?
For a point charge, the electric flux through any closed surface surrounding the charge is constant and equal to q/ε₀, where q is the charge and ε₀ is the permittivity of free space. This is a direct application of Gauss's law and is independent of the surface's shape or size, as long as it encloses the charge.
11. How does electric flux change with distance from a point charge?
The total electric flux through a closed surface around a point charge remains constant regardless of distance. However, the flux density (flux per unit area) decreases with increasing distance because the same total flux is spread over a larger surface area, following an inverse square relationship.
12. What's the difference between electric flux density and electric flux?
Electric flux density, also known as electric displacement, is the amount of electric flux per unit area (D = Φ/A). It's a vector quantity measured in coulombs per square meter (C/m²). Electric flux, on the other hand, is the total flow of the electric field through an entire surface, measured in volt-meters (V⋅m).
13. How does electric flux behave in dielectric materials?
In dielectric materials, the electric flux is affected by polarization. The total flux (of electric displacement) remains proportional to the free charge, but the flux of the electric field is reduced due to the opposing field created by the aligned dipoles in the dielectric.
14. What's the relationship between electric flux and electric displacement?
Electric displacement (D) is related to electric field (E) and polarization (P) by D = ε₀E + P. The flux of electric displacement through a closed surface is equal to the free charge enclosed, regardless of the medium. This concept extends Gauss's law to dielectric materials.
15. Can electric flux be infinite?
In theory, electric flux could approach infinity for an infinitely large charge or an infinitely strong electric field. However, in practical, physical situations, electric flux is always finite because charges and field strengths have physical limits.
16. Can electric flux be used to determine the direction of an electric field?
Electric flux alone cannot determine the direction of an electric field because flux is a scalar quantity. However, by measuring the flux through surfaces oriented in different directions, one can infer the field's direction. The surface with the maximum positive flux will be perpendicular to the field direction.
17. What is the formula for electric flux?
The formula for electric flux (Φ) is Φ = E ⋅ A ⋅ cos θ, where E is the magnitude of the electric field, A is the surface area, and θ is the angle between the electric field and the surface normal. For a non-uniform field or irregular surface, we use the integral form: Φ = ∫E ⋅ dA.
18. How does electric flux behave in a uniform electric field?
In a uniform electric field, the flux through a flat surface is simply the product of the field strength, the surface area, and the cosine of the angle between the field and the surface normal (Φ = EA cos θ). This simplifies calculations compared to non-uniform fields.
19. Can electric flux be measured directly?
Electric flux cannot be measured directly like voltage or current. It's a calculated quantity based on measurements of electric field strength, surface area, and the angle between them. In practice, we often measure related quantities like charge or field strength and then calculate the flux.
20. How does the concept of solid angle relate to electric flux?
Solid angle is useful in calculating electric flux, especially for point charges. The flux through a surface subtended by a solid angle Ω at a point charge q is given by Φ = (q/4πε₀)Ω. This relationship simplifies flux calculations for symmetric situations.
21. How does the principle of superposition apply to electric flux?
The principle of superposition applies to electric flux just as it does to electric fields. The total flux through a surface due to multiple charges is the sum of the fluxes due to each individual charge. This principle allows us to break down complex problems into simpler parts.
22. How is Gauss's law related to electric flux?
Gauss's law states that the total electric flux through a closed surface is proportional to the enclosed electric charge. Mathematically, it's expressed as Φ = Q / ε₀, where Φ is the total flux, Q is the enclosed charge, and ε₀ is the permittivity of free space. This law connects the concept of flux to the distribution of electric charges.
23. What's the significance of Gauss's law in calculating electric flux?
Gauss's law is crucial for calculating electric flux because it relates the flux through a closed surface to the enclosed charge. This relationship often simplifies flux calculations, especially for symmetric charge distributions, by allowing us to determine the flux without knowing the exact field at every point.
24. Why is the concept of electric flux important in electromagnetism?
Electric flux is crucial in electromagnetism because it helps describe how electric fields interact with surfaces and charges. It's fundamental to understanding Gauss's law, which relates electric fields to charge distributions. Flux also plays a key role in explaining electromagnetic induction and Maxwell's equations, which form the foundation of classical electromagnetism.
25. How does the concept of electric flux apply to conductors?
In a conductor at electrostatic equilibrium, the electric field inside is zero. Consequently, the electric flux through any closed surface entirely within the conductor is also zero. However, there can be a non-zero flux through surfaces that include the conductor's boundary, where charges accumulate.
26. How does electric flux relate to electric potential?
While electric flux and potential are different concepts, they're related through the electric field. Flux is the integral of the electric field over an area, while potential is the integral of the electric field along a path. Changes in electric potential can lead to changes in electric field, which in turn affect the flux.
27. Can electric flux be negative?
Yes, electric flux can be negative. The sign of the flux depends on the direction of the electric field relative to the surface normal. If the electric field lines are entering the surface, the flux is negative. If they're exiting the surface, the flux is positive.
28. What factors affect the magnitude of electric flux?
The magnitude of electric flux depends on three main factors: the strength of the electric field, the size of the surface area, and the angle between the electric field lines and the surface normal. Increasing the field strength or surface area increases the flux, while the flux is maximum when the field is perpendicular to the surface.
29. Can electric flux exist in a region with no electric field?
No, electric flux cannot exist in a region with no electric field. By definition, electric flux is the measure of the electric field passing through a surface. If there's no electric field, there are no field lines to pass through any surface, resulting in zero flux.
30. What's the difference between electric flux and magnetic flux?
While both are measures of field strength through a surface, electric flux quantifies the flow of electric field lines, while magnetic flux quantifies the flow of magnetic field lines. Electric flux is related to electric charges, while magnetic flux is associated with moving charges or changing electric fields.
31. What's the relationship between electric flux and electric field lines?
Electric flux is directly related to electric field lines. The flux through a surface is proportional to the number of field lines passing through it. More field lines crossing a surface indicate higher flux. The direction of the field lines relative to the surface determines whether the flux is positive or negative.
32. What is the SI unit of electric flux?
The SI unit of electric flux is newton-meter squared per coulomb (N⋅m²/C) or volt-meter (V⋅m). This unit is derived from the definition of flux as the product of electric field (N/C or V/m) and area (m²).
33. What's the significance of electric flux in understanding electromagnetic shielding?
Electric flux is crucial in understanding electromagnetic shielding. A perfect conductor acts as a Faraday cage, with zero electric field (and thus zero flux) inside. By redirecting electric flux around an enclosed space, conductive shields protect sensitive equipment from external electric fields.
34. How is electric flux different from electric field?
Electric flux is a scalar quantity that measures the total amount of electric field passing through a surface, while an electric field is a vector quantity that represents the force per unit charge at a point in space. Flux considers both the field strength and the area it passes through, whereas the field only describes the strength and direction at a specific point.
35. How does electric flux relate to the concept of electric field lines?
Electric field lines provide a visual representation of electric flux. The number of field lines passing through a surface is proportional to the electric flux. Where field lines are dense, the flux is greater. The direction of the field lines indicates whether the flux is entering or exiting a surface.
36. How does electric flux relate to Faraday's law of induction?
Faraday's law of induction states that the induced electromotive force (EMF) in a circuit is equal to the negative rate of change of magnetic flux through the circuit. While this law directly involves magnetic flux, changes in electric flux can induce magnetic fields, linking the two concepts in electromagnetic induction.
37. How does electric flux relate to the concept of electric field energy density?
While electric flux and field energy density are distinct concepts, they're both related to the electric field. The energy density is proportional to the square of the electric field (u = ½ε₀E²), while flux is linearly related to the field. Areas of high flux often correspond to regions of high energy density.
38. Can electric flux be used to determine the direction of induced electric fields in electromagnetic induction?
While electric flux itself doesn't determine the direction of induced fields, changes in magnetic flux induce electric fields according to Faraday's law. The direction of these induced electric fields is such that they create a magnetic field opposing the change in magnetic flux, as described by Lenz's
39. Can electric flux be conserved?
Electric flux is not a conserved quantity in the same way that charge or energy is conserved. The total flux through a closed surface can change if the enclosed charge changes. However, in a static situation with no change in charge distribution, the flux remains constant.
40. How does electric flux relate to Coulomb's law?
While Coulomb's law describes the force between point charges, electric flux is more closely related to Gauss's law. However, both laws stem from the same fundamental principles of electrostatics. The electric field used in flux calculations can be derived from Coulomb's law for point charges.
41. What's the significance of Gauss's law in integral form?
Gauss's law in integral form, ∮E⋅dA = Q/ε₀, relates the electric flux through a closed surface to the enclosed charge. This form is particularly useful for calculating electric fields in situations with high symmetry, where direct integration of Coulomb's law would be difficult.
42. How does electric flux behave in a time-varying electric field?
In a time-varying electric field, the electric flux also varies with time. This changing electric flux can induce a magnetic field, as described by Maxwell's equations. The relationship between changing electric flux and induced magnetic fields is fundamental to electromagnetic wave propagation.
43. Can electric flux be negative inside a Gaussian surface?
The net electric flux through a closed Gaussian surface is always positive if the enclosed charge is positive, and negative if the enclosed charge is negative. However, the flux through a portion of the surface can be negative if the electric field lines enter that portion of the surface.
44. What's the relationship between electric flux and charge density?
Electric flux is directly related to charge density through Gauss's law. For a volume charge density ρ, the flux through a closed surface is given by Φ = ∫ρdV/ε₀, where the integral is over the volume enclosed by the surface. This relationship allows us to determine charge distributions from flux measurements.
45. How does the concept of electric flux apply to spherical symmetry?
In spherically symmetric charge distributions, like point charges or uniformly charged spheres, the electric flux through any spherical surface centered on the charge is constant and equal to q/ε₀, regardless of the sphere's radius. This is a powerful application of Gauss's law.
46. Can electric flux be used to determine the magnitude of an electric field?
Yes, electric flux can be used to determine the magnitude of an electric field, especially in situations with high symmetry. By applying Gauss's law and choosing an appropriate Gaussian surface, we can relate the flux to the enclosed charge and then calculate the field magnitude.
47. How does electric flux behave at the interface between two different dielectric materials?
At the interface between two dielectrics, the normal component of the electric displacement (D) is continuous, while the normal component of the electric field (E) may be discontinuous. This means the flux of D is continuous across the boundary, but the flux of E may change.
48. What's the significance of the divergence theorem in understanding electric flux?
The divergence theorem relates the flux of a vector field through a closed surface to the divergence of the field within the volume enclosed by the surface. In electrostatics, this theorem allows us to express Gauss's law in differential form, connecting the divergence of the electric field to charge density.
49. Can electric flux be used to detect the presence of hidden charges?
Yes, electric flux can be used to detect hidden charges. By measuring the flux through a closed surface surrounding a region, we can determine if there's a net charge inside, even if we can't directly observe the charges. This principle is used in various electromagnetic sensing technologies.
50. How does the concept of electric flux apply to cylindrical symmetry?
In systems with cylindrical symmetry, like long charged wires or cylinders, the electric flux through a cylindrical Gaussian surface is often constant per unit length. This symmetry simplifies flux calculations and is useful in determining the electric field for such charge distributions.
51. What's the relationship between electric flux and capacitance?
While not directly related, both electric flux and capacitance involve electric fields and charges. The capacitance of a system is related to the electric field configuration between conductors, which in turn affects the flux. In parallel plate capacitors, for example, the flux between the plates is related to the stored charge.
52. How does electric flux behave in the presence of electric dipoles?
For an electric dipole, the net flux through a closed surface enclosing the entire dipole is zero, as the positive and negative fluxes cancel out. However, if the surface only encloses one end of the dipole, there will be a non-zero flux. This behavior is crucial in understanding polarization in dielectrics.
53. Can electric flux be used to understand the behavior of conductors in electrostatic equilibrium?
Yes, electric flux is useful in understanding conductor behavior. In electrostatic equilibrium, the electric field inside a conductor is zero, meaning there's no flux through any closed surface entirely within the conductor. All excess charge resides on the surface, creating flux only through surfaces that include the conductor's boundary.
54. How does the concept of electric flux apply to planar symmetry?
In systems with planar symmetry, like infinite charged planes, the electric flux through a surface parallel to the plane is constant per unit area. This symmetry allows for straightforward flux calculations and is useful in determining electric fields for planar charge distributions.
55. How does electric flux relate to the concept of electric field lines in three dimensions?
In three dimensions, electric flux can be visualized as the number of field lines passing through a surface. The flux through a closed surface is proportional to the net number of field lines leaving (or entering) the surface. This 3D perspective helps in understanding complex field configurations and charge distributions.

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