Question

A cube is made from six thin insulating square faces, each square having side $d$ and carrying a uniformly distributed charge of $Q$ . The magnitude of electric flux leaving the sixth face, due to the electric field of other five faces, is $\varphi$ . The magnitude of electrostatic force on each face of cube is $F$ . Then,

• A. $\varphi =\frac{5Q}{6{ϵ}_0}$
• B. $\varphi =\frac{Q}{2{ϵ}_0}$
• C. $F=\frac{2Q^2}{{ϵ}_0{d}^2}$
• D. $F=\frac{Q^2}{{ϵ}_0{d}^2}$

Answer 1

Answer: (B)

Self leaving flux on each face $={\varphi }^{\prime }$
$\varphi +{\varphi }^{{}^{\prime }}=\frac{Q}{{ϵ}_0}\Rightarrow \varphi ={\varphi }^{{}^{\prime }}=\frac{Q}{2{ϵ}_0}$
$F=\sigma \int EdAcos\theta =\sigma \frac{Q}{2{ϵ}_0}=\frac{Q^2}{2{ϵ}_0{d}^2}$