question_answer

A point charge \[+20\mu C\] is at a distance 6 cm directly above the centre of a square of side 12 cm as shown in figure. The magnitude of electric flux through the square is:

A) \[2.5\times {{10}^{6}}N{{m}^{2}}{{C}^{-1}}\]

B) \[3.8\times {{10}^{5}}N{{m}^{2}}{{C}^{-1}}\]

C) \[4.2\times {{10}^{5}}N{{m}^{2}}{{C}^{-1}}\]

D) \[2.9\times {{10}^{6}}N{{m}^{2}}{{C}^{-1}}\]

Correct Answer: B

Solution :

(b) \[3.8\times {{10}^{5}}N{{m}^{2}}{{C}^{-1}}\] From figure, it is clear that square ABCD is one of the six faces of a cube of side 12 cm. By Gauss's theorem, total electric flux through all the six faces of the cube\[=\frac{q}{{{\varepsilon }_{0}}}\] \[\therefore \]Electric flux through the square \[\phi =\frac{1}{6}\frac{q}{{{\varepsilon }_{0}}}=\frac{1}{6}\times \frac{20\times {{10}^{-6}}}{8.85\times {{10}^{-12}}}\] \[=3.8\times {{10}^{5}}\,N{{m}^{2}}{{C}^{-1}}\]