How is electric flux related to Gauss law

The electric field is the field that surrounds electrically charged particles. And electric flux is the rate that determines the flow of that electric charge through an area. And this rate is directly proportional to the number of lines passing through the surface. These lines are said to emerge from a positive charge and terminate in a negative charge. This article elaborates on how electric flux is related to Gauss law. 

What is Electric Field Lines?

As per the electric flux related to Gauss, imaginary lines drawn to understand the concept of the electric field in a better way are known as electric field lines or electric force lines, some rules are used to represent these lines graphically. 

• The direction field at any point on a field line is given by a tangent drawn at that point.

• It starts with a positive charge and sinks to a negative charge.

• It can be either a straight or curved line.

• It can’t possibly be a closed curve.

• Because electric field lines cannot emerge and sink from the same point, they cannot be closed lines.

• Two electric field lines cannot cross each other.

• This is because the electric field line also represents the direction of the electric field lines at a specific point. The electric field can only have one direction, and if it intersects, it means that there is a two-directional, so electric field lines cannot intersect.

What is electric flux?

According to the electric flux related to Gauss law, you can say electric flux is the number of lines passing through a surface. It is also used to define the strength of the electric field from a distance creating a charge. This electric field E generates a force on an electric charge at any point. 

When the plane is normal, the flow of the electric field, the flux is 

Φ= EA

For a uniform electric flux passing through a surface of area S is, 

Φ= E.A = EAcosθ

Where E is the magnitude of the electric field, S is the surface area, and θ is the angle between electric field lines and the normal. 

The electric flux dΦE through a small surface area dS in a non-uniform electric field is given by dΦE=EdS. (the electric field, E, multiplied by the component of area perpendicular to the field).

The SI unit of electric flux is volt per meter. This volt per meter equals Newton-meters square coulomb inverse (N m2 C-1). The basic unit of electric flux is kg·m3·s-3·A-1. 

Properties of Electric flux

The electric flux that arises when electric flux lines pass through a surface has the following characteristics:

• Flux lines frequently have positive charges at the start and negative charges at the end.

• The number of flux lines determines the frequency of the electric field. 

• All the flux lines are parallel to one another.

• Usually, flux lines enter or exit a charged surface. 

Gauss Law

To understand electric flux related to Gauss law importance, let’s first look at Gauss Law. 

Gauss Law defines the static electric field generated by the distribution of electric charges. It asserts that the electric flux across any closed surface is dependent on the total electric charge enveloped by this surface. 

The law explains the connection between an electric charge and the resulting electric field. Gauss’ law gives us one of the four fundamental equations that regulate electromagnetically. The other three are Gauss’s law, Faraday’s law, and Ampere’s law. 

Notes on how is electric flux related to Gauss law?

Gauss Law explains that electric flux through a closed Gaussian surface equals the total charge inside the surface divided by permittivity (ε0).  

Gauss law in integral form can be given as: 

∫E⋅dA = Q/ε0

Where,

E defines the electric field vector

Q defines the enclosed electric charge

ε0 is the electrical permittivity of free space

A is the outward pointing vector.

The Gauss theorem also states that electric flux from any closed surface results from sources and sinks of the electric field enclosed by the surface. 

Any charges situated outside the surface do not contribute to the electric flux. 

And the source and sink in a formula are only electric charges. For example, changing magnetic fields cannot act as sources or sinks. 

Application of Gauss Law

Now that your know-how is electric flux related to Gauss law let’s look at the application of Gauss Law. 

• Gauss law can find electric fields due to the infinitely long straight charged wire. 

• It can also calculate electric fields due to an infinitely charged plane sheet. 

• Gauss law can also be applied to find electric fields due to two parallel charged sheets. 

• It is also used to find an electric field in a uniformly charged spherical shell. 

Conclusion

Gauss law explains that the amount of flux in a closed surface equals the charge enclosed and is divided by the permittivity. This article has explained how electric flux is related to the Gauss law. Electric field lines and electric flux are all significant components of Gauss Law. Gauss law also explains that electric flux passing through a closed surface is independent of the shape and area of the surface.