Question

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

Answer 1

The correct option is 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 $12cm$.

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$

$\varphi =\frac{1}{6}\frac{q}{{\epsilon }_0}=\frac{1}{6}\times \frac{20\times {10}^{-6}}{8.85\times {10}^{-12}}=3.8\times {10}^{5}N{m}^2{C}^{-1}$