Unit of Electric Flux

Introduction

The atom was known to be electrically neutral through the pioneering studies of scientists such as J.J. Thomson and A. Rutherford who carried out their research in the late 19th and early 20th centuries. An atom consists of elementary electric charges. The force between electric charges is called electric force. This force belongs to the type of non-contact force. Because this force works without the charges touching each other.

The area around a charge where its effect can be felt is called an electric field. The direction of the electric field is known as the direction of force acting on a small positive charge placed in the field. Hence, the lines representing the electric field are called lines of force. Lines of charge are straight or curved lines drawn in the direction in which a uniform electric charge tends to move in an electric field. They are imaginary lines.

What is Electric Flux?

The number of electric field lines obtained in the specified surface when electric field lines flow through that surface is called Electric flux. It can take a positive or negative value. Figure 1 can be used to easily understand what is electric flux.

Fig.1. Electric Flux

The electric field of a point electron is shown in the figure. Let us consider two small rectangular-shaped surfaces perpendicular to the field in regions A and B. The area of both A and B is equal, the number of electric field lines crossing the rectangle in area B is greater than the number of electric field lines crossing the rectangle in area B. As the electric field strength of a point electron decreases with increasing distance from the electric charge, its electric flux also decreases with increasing distance. The concepts we have seen so far will help to form a qualitative idea about the power flow. However, a precise definition of the current is required.

Units and Dimension of Electric flux

The SI unit of electric flux is $\mathrm{Nm^{2}C^{−1}}$ . It is a scalar quantity.

$\mathrm{[ML^{3}T^{−3}\:A^{−1}]}$ is the dimensional expression of electric flux.

The Formulae of Electric Flux

The Electric Flux of a Uniform Electric Field

Let us assume a constant electric field around space. Let us take a surface A perpendicular to the electric field lines as given in the figure.

Fig.2. Electric flux in uniform electric Field

For this case, electric flux is

$$\mathrm{\Phi_{E}=EA}$$

If surface A is placed parallel to a constant electric field, the electric field lines flowing inside the surface become zero, For this case, the electric flux is

$$\mathrm{\Phi_{E}=0}$$

When the electric field makes an angle θ with the surface only the electric field lines which are in the vertical direction to the surface give an electric flux. The surface does not give an electric flux when it is placed parallel. The electric flux in this case

$$\mathrm{\Phi_{E}=(Ecos\:θ)\:A}$$

Here the angle between the direction of the electric field and the direction of the vertical line drawn to the surface is θ. Therefore, as a general definition, the flux in a constant electric field is defined as

$$\mathrm{\Phi_{E}=\overrightarrow{E}.\overrightarrow{A}=EAcos\:θ}$$

Note that $\mathrm{\overrightarrow{A}=A\widehat{n}}$ here. Its numerical value is A and its unit vector perpendicular to its surface is $\mathrm{\widehat{n}}$. According to this definition, $\mathrm{\Phi_{E}=\overrightarrow{E}.\overrightarrow{A}}$

The Electric Flux of a Non-uniform Electric Field

$$\mathrm{\Phi_{E}=\oint\:\overrightarrow{E}.\overrightarrow{dA}}$$

From the above equation, the electric field that flows through a surface determines the electric flux through a given surface and the direction of the electric flux.

Electric Flux in a closed Surface

The electric flux for a closed surface is represented by the following formulae.

$$\mathrm{\Phi_{E}=\oint\:\overrightarrow{E}.\overrightarrow{dA}}$$

The summation used in the above equation is a closed or closed area summation, and the outward vertical line drawn for each surface element in it is the direction of $\mathrm{\overrightarrow{dA}}$

The values of total electric flux through a surface will be positive, negative, or zero. In general, if the field lines enter a closed surface, the flux is negative and if they leave the closed surface, the flux is positive.

Applications

• An Electric field is determined by electric flux.

• The complex figures of an electric field are evaluated by the electric flux

• In electrostatics, the gauss theorem is the major part of electrostatics and it depends on electric flux.

Solved Examples

Example 1: If the rectangle of sides 5 cm and 10 cm is placed in a constant electric field of $\mathrm{100\:NC^{−1}}$, calculate the electric flux through the rectangle surface. The given angle is $\mathrm{θ=60^{\circ}}$. Calculate the electric flux when θ is zero.

Solution:

Electric Flux,

$$\mathrm{\Phi_{E}=\overrightarrow{E}.\overrightarrow{A}=EAcos\:θ}$$

$$\mathrm{=100\times5\times10\times10^{−4}\times\:cos60^{\circ}}$$

$$\mathrm{\Phi_{E}=0.25\:Nm^{2}\:C^{−1}}$$

If $\mathrm{θ=0^{\circ}}$ , Electric flux is

$$\mathrm{\Phi_{E}=\overrightarrow{E}.\overrightarrow{A}=EAcos\:0^{\circ}}$$

$$\mathrm{=100\times5\times10\times10^{−4}\times\:1}$$

$$\mathrm{cos\:0^{\circ}=1}$$

$$\mathrm{\Phi_{E}=0.5 Nm^{2} C^{−1}}$$

Conclusion

The area around a charge where its effect can be felt is called an electric field. The direction of the electric field is known as the direction of force acting on a small positive charge placed in the field.

The number of electric field lines passing through a specified surface when placed in an electric field is called Electric flux. It can take a positive or negative value. In general, if the field lines enter a closed surface, the flux is negative and if they leave the closed surface, the flux is positive.

FAQs

Q1. What is electrical energy?

Ans. The work done to move electric charges or the amount of work done by the circulation of electric current in an electric circuit determines the electrical energy.

Q2. Define electric dipole

Ans. Two equal, unlike charges are divided by a small distance from an electric dipole. In many molecules, the center of positive charge and the center of negative charge do not coincide. Such molecules act like stable electric dipoles.

Q3. What causes the magnetic flux reversal?

Ans. Magnetic flux reversal is accomplished by relative motion in the middle of the circuit and magnet, change in the current flowing in the adjacent circuit.

Q4. Define kilowatt hour.

Ans. Measuring electrical energy in the small unit of watt second requires dealing with large numerical values. Therefore, electrical energy is measured in units of a kilowatt-hour. Kwh is the unit of energy; Is not a unit of Power.

Q5. What is a volt?

Ans. The electromotive force of an electric source is the work done (W) by a unit of charge once moving around a circuit. Both electromotive force and potential difference have the same SI unit ‘volt’.