Question

What is meant by electric flux? Write its SI unit and dimensional formula.

Answer 1

Hint: Define electric flux at first and give the symbol by which it is represented. Then according to the question write the SI unit of electric flux and from that SI unit find the individual dimensions of the units and then do the dimensional analysis to get the dimensional value of electric flux.

Complete step-by-step answer:
The rate of flow of the electric field or the measure of the distribution of the electric field through a given area is known as electric flux. Electric field strength at any distance from the charge causing the field is known as electric flux . It is expressed using the Greek symbol Phi: $\phi$
Electric flux is the property of an electric field that is the number of electric field lines that intersect a given area. It is represented as
$\Delta {{\phi }_{e}}=\vec{E}.\Delta \vec{A}$
In the above equation, E is the electric field intensity and A is the vector area.
The SI base unit of electric flux is voltmeters (V m) which is also equal to newton-meters squared per coulomb ($N{{M}^{2}}{{C}^{-1}}$).
Electric flux associated with any surface is defined as the dot produced or scalar of
Aerial vector $(\overrightarrow{ds})$ and electric field vector $(\vec{E})$ of that surface.
Now, we know that the SI unit of electric flux is($N{{M}^{2}}{{C}^{-1}}$).
[M] = MASS.
[L] = LENGTH.
[T] = TIME.
[ I ] = CURRENT
Therefore we know that ‘N/Newton’ the SI unit of force is represented in dimension as $ML{{T}^{-2}}$ ,
${{M}^{2}}$the SI unit of meter / Length is represented in dimension as ${{L}^{2}}$ .
And ‘C’ the SI unit of charge is represented in dimension as ${{M}^{0}}{{L}^{0}}{{T}^{1}}{{I}^{1}}$,
Therefore on placing the dimensional values in the SI unit of electric flux ($N{{M}^{2}}{{C}^{-1}}$) we get,
$M{{L}^{3}}{{T}^{-3}}{{I}^{-1}}$ (Answer) .

Note: Remember that SI unit of flux can be represented in two ways. While doing dimensional analysis remember to break all the units for dimensional analysis into single pieces and then do the analysis. This process avoids small mistakes that are done by students in the examination hall.