Question

A charge q is placed at the corner of a cube of side a. The electric flux passing through the cube is:
A. $\dfrac{q}{{a{\varepsilon _0}}}$
B. $\dfrac{q}{{{\varepsilon _0}{a^2}}}$
C. $\dfrac{q}{{4\pi {\varepsilon _0}{a^2}}}$
D. $\dfrac{q}{{8{\varepsilon _0}}}$

Answer 1

To cover the cube place identical cubes beside and above the cube. So the charge comes at the centre 8 such cubes. Electric flux will be divided in 8 cubes. Use Gauss law, to find the electric flux passing through the cube.

Complete step by step answer:
We are given that a charge q is placed at the corner of a cube of side a.
We have to find the electric flux passing through the cube.
According to the Gauss law, the total flux from a charge q is $\dfrac{q}{{{\varepsilon _0}}}$
If the charge is on the corner of a cube, some of the flux enters the cube and leaves through some of its faces. But some of the flux doesn't enter the cube.
So we have to cover the cube. If the charge is at the very centre of this hypothetical cube then it is on a corner of each of the 8 cubes. An equal amount of flux will spread outwards through each of the cubes.
The fluxed will be shared between 8 cubes.
Therefore, the electric flux passing through one cube will be
$\dfrac{1}{8} \times \dfrac{q}{{{\varepsilon _0}}} = \dfrac{q}{{8{\varepsilon _0}}}$
The correct option is Option D.
When a charge q is placed at the corner of a cube of side a then the electric flux passing through the cube will be $\dfrac{q}{{8{\varepsilon _0}}}$

Note: A cube is a three-dimensional solid object bounded by six square sides with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices. Electric flux is a number of electric lines of forces which passes through any cross sectional area when the cross sectional area is kept perpendicular to the direction of electric field.