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. Zero

Answer 1

Answer: (A)

$\frac{Q}{{\epsilon }_0}$

For five faces of cube other than ABCD,

$\Rightarrow {\varphi }_1=5\times \frac{Q}{6{\epsilon }_0}$
Flux due to charge at P, through face ABCD = through all other five faces

Thus flux due to charge at P through all other five faces,
${\varphi }_2=\frac{Q}{6{\epsilon }_0}$
$\varphi ={\varphi }_1+{\varphi }_2=\frac{Q}{{\epsilon }_0}$.