Question

The flux crossing three faces close to the charge if charge is just inside the cube will be

• A. $\frac{q}{8{\epsilon }_0}$
• B. $\frac{q}{{\epsilon }_0}$
• C. $\frac{7q}{8{\epsilon }_0}$
• D. $\frac{q}{6{\epsilon }_0}$

Answer 1

The correct option is C $\frac{7q}{8{\epsilon }_0}$

As we know if charge is placed it at center of the cube then flux linked with it is $q/{ϵ}_o$ and charge is placed at corner of the cube then flux linked with the cube is $q/8{ϵ}_o$. Now if charge is placed just inside the cube at a corner then total flux linked with cube will become $q/{ϵ}_o$ but for the three symmetric surfaces which are distant from the charge for them charge is still at the corner therefore, flux linked with them is still $q/8{ϵ}_o$ therefore, remaining flux passes through the three symmetric surfaces which are closer to the charge.

Therefore, $q/{ϵ}_o-q/8{ϵ}_o=7q/8{ϵ}_o$

option (C)