Question

Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length ‘$a$’ as shown in the diagram. A charge $+Q$ is placed at the centre ‘$O$’ of the cube. $P$ is such a point outside the cube that the line $OP$ perpendicularly intersects the surface $ABCD$ at $R$ and also $OR=RP=a/2$. A charge $+Q$ is placed at point $P$ also. What is the total electric flux through the five faces of the cube other than $ABCD$ ?

• A. $\frac{Q}{{\epsilon }_0}$
• B. $\frac{5Q}{6{\epsilon }_0}$
• C. $\frac{10Q}{6{\epsilon }_0}$
• D. 0

Answer 1

Answer: (A)

For surface $ABCD$ electric flux is zero. Because at surface $ABCD$ net electric field is zero. Using Gauss's law,
$\oint \Sigma \cdot dS=\frac{Q_{\text{in }}}{{\epsilon }_0}$
Electric flux through the five faces of the cube,
${\varphi }_B=\frac{Q}{{\epsilon }_0}$