Question

The inward and outward electric flux for a closed surface in ${\mathrm{Nm}}^2/\mathrm{C}$are respectively $8\times {10}^3\mathrm{And}4\times {10}^3.$ Then the total charge inside the surface is?

Answer 1

Step 1:Given data:

The inward and outward electric flux for the closed surface in ${\mathrm{Nm}}^2/\mathrm{C}$is given by: $8\times {10}^3$and $4\times {10}^3$

Step 2: Calculation of flux:

The total number of electric field lines passing through a given area in a unit of time is basically defined as the electric flux.

For convention, the inward flux can be taken as negative and the outward flux is always taken as positive.
The total flux, which is denoted by $\varphi$can be given as :

$\mathrm{\varphi }=$Sum of the inward flux for the given closed surface

$$\begin{gathered} =-8\times {10}^3+4\times {10}^3 \\ =-4\times {10}^3\mathrm{N}{\mathrm{m}}^2/\mathrm{C} \end{gathered}$$

Step 3: The formula for Calculation of total Charge inside the surface is:
The formula for flux is basically given as:

$\mathrm{\varphi }=\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

Where,

$\mathrm{q}=$ Enclosed total charge

${\mathrm{\epsilon }}_0=$the permittivity of free space

Hence, the formula total Charge can be written as:

$\mathrm{q}=\mathrm{\varphi }{\mathrm{\epsilon }}_0$

Step 4: Calculation of total Charge inside the surface is:
By substituting the given data, the total Charge inside the surface can be calculated as:
$\Rightarrow \mathrm{q}=\mathrm{\varphi }{\mathrm{\epsilon }}_0$
$\Rightarrow \mathrm{q}=-4\times {10}^3{\mathrm{\epsilon }}_0$
Hence, we can say that the total charge inside the surface is $-4\times {10}^3{\epsilon }_0$.