Question

Electric flux: Scalar or a vector quantity?

Answer 1

Hint:In electrostatics, electric field is the space around an electric charge where any other electric charge can experience electric force, we will first learn the definition of electric flux then determine the nature of electric flux whether it’s a scalar or a vector quantity.

Complete answer:
Electric field is a vector quantity which has a magnitude and a direction (The direction of electric field lines is away from the charge if the charge is positive and direction of electric field lines is towards the charge if charge is negative).Definition of Electric flux states that “Electric flux is the dot product between electric field vector and the area vector” around which electric field lines are passing. Mathematically it’s written as:
${\phi _E} = \vec E.\vec A$
since, electric field is a vector quantity and the area is also a vector quantity, the dot product of two vectors is always a scalar quantity.

Hence, Electric flux is a scalar quantity not a vector quantity.

Additional Information: Electric flux around a closed surface can also be calculated by using the formula that ${\phi _E} = \dfrac{{{Q_{enclosed}}}}{{{ \in _0}}}$ where $Q$ is the total charge inside the closed surface and ${ \in _0} = 8.854 \times {10^{ - 12}}{C^2}{m^{ - 2}}{N^{ - 1}}$ known as permittivity of free space.

Note: It should be remembered that, while calculating electric flux we always take the direction of a surface area as a normal vector of the surface. The SI units of electric flux will be the product of SI unit of electric field and area simple written as $N{C^{ - 1}}{m^2}.$