The inward and outward electric flux for a closed surface in units of Nm^2 / C are respectively

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The inward and outward electric flux for a closed surface in...

The inward and outward electric flux for a closed surface in units of $\mathrm{Nm}^{2} / \mathrm{C}$ are respectively $8 \times 10^{3}$ and $4 \times 10^{3}$. Then the total charge inside the surface is $\ldots \ldots \ldots \ldots . . \mathrm{c}$. (A) $\left[\left(-4 \times 10^{3}\right) / \epsilon_{0}\right]$ (B) $-4 \times 10^{3}$ (C) $4 \times 10^{3}$ (D) $-4 \times 10^{3} \mathrm{E}_{0}$

The inward and outward electric flux for a closed surface in units of $\mathrm{Nm}^{2} / \mathrm{C}$ are respectively $8 \times 10^{3}$ and $4 \times 10^{3}$. Then the total charge inside the surface is $\ldots \ldots \ldots \ldots . . \mathrm{c}$.
(A) $\left[\left(-4 \times 10^{3}\right) / \epsilon_{0}\right]$
(B) $-4 \times 10^{3}$
(C) $4 \times 10^{3}$
(D) $-4 \times 10^{3} \mathrm{E}_{0}$

Key Concepts

Gauss's Law

Gauss's Law is a fundamental principle in electromagnetism that links the net electric flux passing through a closed surface to the total electric charge enclosed within that surface. It states that the net flux is equal to the enclosed charge divided by the vacuum permittivity, thereby providing a direct method to calculate the charge from the measured flux.

Electric Flux

Electric flux represents the number of electric field lines penetrating a given surface. It quantifies the strength and distribution of the electric field through an area and is measured in units of N·m²/C. This concept is essential in understanding how electric fields interact with surfaces.

Net Electric Flux

Net electric flux is the result of subtracting any inward flux from the outward flux through a closed surface. The net flux, which can be positive or negative, indicates the excess of field lines leaving or entering the surface and directly determines the sign and magnitude of the enclosed charge when applying Gauss's Law.

Vacuum Permittivity

Vacuum permittivity, often denoted as ??, is a constant that characterizes the ability of free space to permit electric field lines. It plays a crucial role in Gauss's Law by setting the relationship between the net electric flux and the enclosed charge, effectively scaling the flux to yield the amount of charge.

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