91Ó°ÊÓ

The given area vector of the surface,$\stackrel{→}{A}=(2\widehat{i}+3\widehat{j}){\text{m}}^2$

The electric field,$\stackrel{→}{E}=4\widehat{i}\text{N}/\text{C}$

The electric field,$\stackrel{→}{E}=−4\widehat{j}\text{N/C}$

Electric flux is the property of an electric field that describes the number of electric field lines crossing through a given surface area.

Formula:

The electric flux through a given surface,

${\mathrm{Ï•}}_E=\stackrel{→}{E}.\stackrel{→}{A}$…..(¾±)

The amount of electric flux through the given area if the electric field is given as

$\stackrel{→}{E}=4\widehat{i}\text{N}/\text{C}$

His is calculated using the given data in equation (i) as follows:

$\begin{array}{c}{\mathrm{Ï•}}_E=(4\widehat{i}\text{N}/\text{C})\left((2\widehat{i}+3\widehat{j}){\text{m}}^2\right)\\ =8.0\text{N}â‹\dots {\text{m}}^2/\text{C}\end{array}$

Hence, the value of the electric flux is $8.0\text{N}â‹\dots {\text{m}}^2/\text{C}$.

The amount of electric flux through the given area if the electric field is given as.

$\stackrel{→}{E}=4\widehat{j}\text{N/C}$

This is calculated using the given data in equation (i) as follows:

$\begin{array}{c}{\mathrm{Ï•}}_E=(4\widehat{j}\text{N}/\text{C}).\left((2\widehat{i}+3\widehat{j}){\text{m}}^2\right)\\ =12.0\text{N}â‹\dots {\text{m}}^2/\text{C}\end{array}$

Hence, the value of the electric flux is $12.0\text{N}â‹\dots {\text{m}}^2/\text{C}$.