Question

A charge $\mathrm{Q}$ is situated at the centre of a cube. The electric flux through one of the
faces of the cube is
A.$\text{Q }/{{\epsilon }_{0}}$
B.$\text{Q }/2{{\epsilon }_{0}}$
C.$\text{Q }/4{{\epsilon }_{0}}$
D.$\mathrm{D} \quad \mathrm{Q} / 6 \mathrm{e}_{0}$

Answer 1

Hint: We are going to apply the idea of Gauss's electric flux law to solve this issue. Under Gauss's electric flux law, we get: $\phi=\dfrac{Q}{\varepsilon {\circ}}$. The flux of the electric field E through any enclosed surface, also known as the Gaussian surface, according to Gauss' theorem, is proportional to the net charge enclosed divided by the permittivity of free space.
Formula used:
$\phi=\dfrac{Q}{\varepsilon {\circ}}$

Complete answer:
The electric field law of Gauss defines the static electric field generated by the distribution of electric charges. The law of Gauss is a general law applied to any enclosed floor. It is an important tool as it allows the measurement of the volume of the enclosed charge to be carried out by mapping the surface area outside of the charge application. The measurement of the electrical field is simplified for geometries with sufficient symmetry. Electric flux, the electric field property that can be considered to be the number of electric power lines (or electric field lines) that intersect a given area. The negative flux is equal in magnitude to the positive flux, so zero is the net or cumulative electrical flux.
We know that total flux passing through the cube is:
$\phi=\dfrac{q}{\varepsilon_{o}}$
As the charge is symmetrically positioned on each face of the square, the electrical flux flowing through each face is proportional to the $\dfrac{1}{6}^{t h}$ of the total flux.
Therefore, electric flux passing through each face $\phi^{\prime}=\dfrac{\phi}{6}=\dfrac{q}{6 \varepsilon_{o}}$
Hence, the electric flux passing through each face to the cube is $\dfrac{q}{6 \varepsilon_{0}}$.

So, the Correct option is (D) .

Note:
Electrical flux is the measure of the electric field through a given surface in electromagnetism, although an electrical field cannot flow by itself. It is a way of describing the strength of the electric field at any distance from the field-causing charge. We have to remember the electric flux formula here. We also have to be careful when writing the denominator and the numerator.