Introduction

The electric field lines qualitatively describe the electric field in any particular region. It can only give qualitative but not any quantitative ideas. It can give relative strength to different fields too. The Gauss law, on the other hand, gives a qualitative and quantitative idea related to any electric field.

Electric Flux

Let E be the magnitude of the electric field perpendicular to the surface area A . Then the electric flux through the surface is given by: Ω=E.A

The SI unit of electric flux is Nm2C-1. The electric flux is directly proportional to the number of field lines passing through the surface area.

If the surface is not perpendicular to the field lines, the flux through the conductor is lesser than given by the equation (as they are dot products). The surface area normal to the surface is always taken under consideration. Let A be the actual surface, and ፀ be the angle between the surface and electric field lines then the electric flux through the surface area is defined as:

Ω=E*A’=EAcosፀ

In this scenario, it is assumed that the field lines are uniform throughout. So, the equation holds good either for some uniform field lines or a very small elementary surface area, say △ A.

In that latter case, the flux through the surface is defined as:

ф=ഽ E*dA

Illustrations: Let a point charge q be placed on the corner of a square. Calculate the flux through the surface.

If point charge, q, is placed on the corner, the field is uniform throughout. But since it is placed on the corner, there exists no electric field perpendicular to the square and coming out of the point charge. Hence the flux through the surface is 0.

Gauss law

Gauss law states that the electric flux through any closed surface is proportional to the total electric charge enclosed in it. Mathematically it is defined as follows:

ф=ഽ E*dA=q/ε

The Gauss law is an alternative form of Coulomb’s law. But it gives a different way to calculate the relationship between electric charge and electric field.

The surface around which the electric flux is being calculated is known as the Gaussian surface. It is imaginary. In real life, there is no boundary representing the Gaussian surface.

Important features of Gaussian law

1. The electric field on the left-hand side is the total electric field contributed by all the charges both inside and outside the Gaussian surface.
2. The charge q appearing on the right-hand side of the equation is the total charge contributed by only the charge contained inside the conductor.
3. The total contribution of the charges present outside the Gaussian surface is 0 to the electric flux.
4. Gaussin surface around any physical body is not unique. We can define any surface around the physical object. The only restriction is that it should be a closed surface.
5. The flux through the Gaussian surface is directly proportional to the number of field lines passing through the surface. The greater the density of the field lines, the greater will be the magnitude of the electric flux.
6. If the net flux through any Gaussian surface is 0, it does not mean the electric field through the surface is 0, but the algebraic sum of the charges inside the surface must be 0.
7. The electric flux through a Gaussian surface does not depend on the configuration of the charges present inside it. However, the electric field inside the surface changes due to the configuration change.

Application of the Gaussian law

1. The Gaussian surface does not need to be any physical surface or body. It is an imaginary geometrical surface and can be empty space, a solid body, or both.
2. We can calculate the electric flux through this law analytically only if the Gaussian surface and the charge distribution have some form of symmetry. Otherwise, it can be calculated with only computers.
3. To find the electric field at any particular point, we need to select a Gaussian surface that passes through it.

Conclusion

 Electric flux passing through a surface area A is defined as the product of surface area A and the electric field E. the electric field and the surface area must be perpendicular to each other. The relation is valid only for the uniform distribution of electric fields. This is an alternative law to Coulomb’s law. It expresses Coulomb’s law and the relationship between electric charges and electric fields in a different way. It states that the total electric flux through any closed surface is directly proportional to the electric charge enclosed within the surface. This law is mainly useful for calculating the elected flux, or electric charge, through surfaces that have some symmetrical property. While the electric field appearing on the left-hand side of the equation contains an electric field due to all the charges, the right-hand side charge is the total charge contributed by all the charges present inside it.