Question

Consider a uniform electric field $E=3 \times 10^{3} \hat{i} N / C .$ What is the flux of this field through a square of $10 \,cm$ on a side whose plane is parallel to the $y-z$ plane?

• A. $10 \,N C ^{-1} m ^{2}$
• B. $20\, N C ^{-1} m ^{2}$
• C. $30 \,N C ^{-1} m ^{2}$
• D. $40\, N C ^{-1} m ^{2}$

Answer 1

Answer: (C)

Here, $\vec{E}=3 \times 10^{3} \hat{i} N / C$
i.e., field is along $+x$ -axis direction.
Surface area, $S=(10 \,cm )^{2}=10^{2} cm ^{2}$
$=10^{2} \times 10^{-4} m ^{2}=10^{-2} m ^{2}$.
When plane is parallel to $y-z$ plane, $\theta=0^{\circ}$
$\phi_{E}=E S \,\cos \,\theta=3 \times 10^{3} \times 10^{-2} \cos 0^{\circ}$
$=30 \,N C ^{-1} m ^{2}$