Question

Given a uniform electric field $\overrightarrow{E}=2\times {10}^3\hat{i}$N/C. Find the flux of this field through a square of side 20 cm, whose plane is parallel to the y-z plane. What would be the flux through the same square, if the plane makes an angle of ${30}^o$ with the x-axis?

Answer 1

$\overrightarrow{E}=2\times {10}^3\hat{i}\left(\frac{N}{C}\right)Flux=\overrightarrow{E}.\overrightarrow{S}=EScos\theta$

When plane is parallel to Y-Z plane then $\theta =0$

Flux =$ES=2\times {10}^3\times {(20\times {10}^{-2})}^2=2\times {10}^3\times 4\times {10}^{-2}=80$

when plane makes angle 30 degree with X axis then perpendicular to plane makes angle 60 degree to X axis

hence

$\theta ={60}^{0}Flux=ES=2\times {10}^3\times {(20\times {10}^{-2})}^2\times cos{60}^0$

=$2\times {10}^3\times 4\times {10}^{-2}\times \frac{1}{2}=40$