Question

A charge q is placed at the center of a cubical box of side a with the top open. The flux of the electric field through one of the surface of the cubical box is

Answer 1

Step 1: Given data

Cubical box:

1. A cubical box is a cube.
2. It is a 3D solid object with six square faces.
3. All the sides of it are of the same length.
4. It is also known as a regular hexahedron.

A diagram to represent the cubical box:

Step 2:

On the basis of the question:

Because the charge is placed at the center of the box.

So, ${\varnothing }_{eachface}=\frac{1}{6}{\varnothing }_{total}$

Now, if the box is complete then the total flux passing through it will be

$=\frac{q}{{\in }_{\circ }}$

But it has one face missing so,

flux$=5\times \frac{1}{6}\frac{q}{{\in }_{\circ }}$

Hence, $\frac{5q}{6{\in }_{\circ }}$