Question

A point charge $+20\mu C$ is at a distance $6cm$ directly above the centre of a square of side $12cm$ as shown is 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. $2.9\times 10^{6}N{m}^2{C}^{-1}$

Answer 1

Answer: (B)

From figure, it is clear that square $ABCD$ is one of the six faces of a cube of side $12cm$.

By Gauss’s theorem, total electric flux through all the six faces of the cube $=\frac{q}{{\epsilon }_0}$
$\therefore$ Electric flux through the square
$\varphi =\frac{1}{6}\frac{q}{{\epsilon }_0}$
$=\frac{1}{6}\times \frac{20\times 10^{-6}}{8.85\times 10^{-12}}$
$=3.8\times 10^{5}N{m}^2{C}^{-1}$