Question

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 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 $12\,cm$.

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
$\phi=\frac{1}{6}\frac{q}{\varepsilon_{0}}$
$=\frac{1}{6}\times\frac{20\times10^{-6}}{8.85\times10^{-12}}$
$=3.8\times10^{5}\,N\,m^{2}\,C^{-1}$