Given a uniform electric field $\to E = 5 \times 10^{3} ˆ i N / C$ , find the flux of this field through a square of 10 cm on a side whose plane is parallel to the y-z plane. What could be the flux through the same square if the plane makes $30^{o}$ angle with the x-axis?

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Solution

Flux through a surface is given by:
$ϕ = \to E . \to d S$

Area is $S = E S c o s (90) = 0.1 \times 0.1 = 0.01 m^{2}$
$ϕ = 5 \times 10^{3} \times 0.01 = 50 N m^{2} C^{- 1}$

When the square makes an angle of $30^{o}$ with the x-axis, angle made by the normal with electric field is $90^{o} - 30^{o} = 60^{o}$
Hence, $ϕ = E S c o s (60^{o}) = 25 N m^{2} C^{- 1}$

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