Question

Electric flux: scalar or a vector quantity?

Answer 1

Electric flux:

1. Electric flux is defined as the total number of electric field lines traversing a specific area in a particular amount of time.
2. Thus, the number of field lines traveling across a specific area in a unit of time determines the electric flux.
3. The electric flux is a dot product and the dot product of two vectors is a scalar quantity, thus, the electric flux is a scalar quantity.

Mathematically, the magnitude of electric flux can be represented as:

$\mathrm{\Delta \varphi }=\int \overrightarrow{\mathrm{E}}.\mathrm{d}\overrightarrow{\mathrm{A}}$

For plane surface and uniform electric field, the above formulation becomes:

$$\begin{gathered} \mathrm{\Delta \varphi }=\overrightarrow{\mathrm{E}}.\overrightarrow{\mathrm{A}} \\ =\mathrm{EAcos\theta } \end{gathered}$$

Where, $\mathrm{E}$ is the magnitude of the electric field, $\mathrm{A}$is the area of the surface through which the electric flux is to be calculated, and $\mathrm{\theta }$ is the angle made by the plane and the axis parallel to the direction of flow of the electric field.

Therefore, electric flux is a scalar quantity.