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 $\phi$ . The magnitude of electrostatic force on each face of cube is $F$ . Then,

• A. $\phi=\frac{5 Q}{6 \epsilon _{0}}$
• B. $\phi=\frac{Q}{2 \epsilon _{0}}$
• C. $F=\frac{2 Q^{2}}{\epsilon _{0} d^{2}}$
• D. $F=\frac{Q^{2}}{\epsilon _{0} d^{2}}$

Answer 1

Answer: (B)

Self leaving flux on each face $=\phi'$
$\phi+\phi^{'}=\frac{Q}{\epsilon _{0}}\Rightarrow \phi=\phi^{'}=\frac{Q}{2 \epsilon _{0}}$
$F=\sigma \displaystyle \int EdAcos\theta =\sigma \frac{Q}{2 \epsilon _{0}}=\frac{Q^{2}}{2 \epsilon _{0} d^{2}}$