What is an Electric Flux?

Electric flux is a property of the electric field. An electric charge is present in the space. For example, an electron is present in space and it has an electric field surrounding it.

The electric field is represented by electric lines of force or electric field lines. Sometimes this line is also known as the Gauss lines or line of flux.

The density of flux lines shows the strength of the electric field. And it is known as “Electric field density”. It is also defined as the number of field lines per unit area.

Electric field lines start from the positive electric charge and end to the negative charge. Therefore, it creates a close loop.

“The total number of field lines passing through the surface is proportional to the electric flux.”

If the positive charge on space is equal in magnitude to the negative charge, the net charge or total charge on space is zero.

If space has some amount of net charge, the flux through that surface is proportional to the enclosed charge. The flux is positive if the charge is positive and negative if the charge is negative.

Formula of Electric Flux

The mathematical representation of electric flux was given by the Gauss law for the electric field. The symbol of electric flux is ф.

Let’s assume that the surface is perpendicular to flux lines. And the flux is distributed uniformly. If the flux passing through a surface of vector area S.

    \[ \vec{\phi} = \vec{E} \cdot \vec{S} \]

Where E is an electric field.

Electric field (E) and Area (S), both are vector quantities. Hence, the electric flux is also a vector quantity. The magnitude of flux is defined as,

    \[ \phi = E \, S \cos{\theta} \]

Where E and S are the magnitudes of electric field and area respectively. And θ is the angle between the electric field lines and the perpendicular to S.

If the electric field is distributed non-uniformly, the differentiation of the above equation. And it is defined as the differential electric flux dф through a differential area dS,

    \[ d \phi = E \cdot dS \]

The total flux of surface area can be derived by the surface integral of the above equation.

    \[ \phi = \iint_S E \cdot dS \]

For closed Gaussian surface, flux is given by,

    \[ \phi = \oint \oint_S E \cdot dS = \frac{Q}{\epsilon_0} \]


The flux has an SI unit of volt-meter (V-m).

From the Gaussian surface, the electric flux is defined as the ratio of the charge to the permittivity of free space. The unit of electric charge is coulomb and the unit of permittivity is Farad per meter.

Therefore, the unit of electric flux is coulomb per Farad per meter.


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