Question

The length of each side of a cubical closed surface is a. If charge q is situated on one of the vertices of the cube then the flux passing through each face of the cube will be :

• A. $\frac{q}{6{\epsilon }_0}$
• B. $\frac{q}{24{\epsilon }_0}$
• C. $\frac{q}{8{\epsilon }_0}$
• D. zero

Answer 1

Answer: (B)

$\frac{q}{24{\epsilon }_0}$

Think of this cube as one of 8 surrounding the charge.Every face has 4 squares and there are 6 faces, hence total no. of squares are 24. Each of 24 squares which make up the surface of this larger cube gets the same flux as every other one. So,

${\int }_{oneface}E.da=\frac{1}{24}{\int }_{largecube}E.da=\frac{1}{24}.\frac{q}{{ϵ}_0}$ (using Gauss's law)