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A large plane charge sheet having charge density $σ = 2 \times 10^{- 6} C / m^{2}$ lies in the $x - y$ plane. Find the flux of the electric field (in SI unit) through a circular area of radius 1cm lying completely in the region where $x, y, z$ are all positive and with its normal making an angle of $60^{0}$ with the $z - a x i s$ .

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answer is 17.74.

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Detailed Solution

$E l e c t r i c f i e l d n e a r t h e p l a n e c h a r g e s h e e t, E = \frac{σ}{2 \in_{0}}$

$T h e a r e a Δ S = π r^{2} = 3.14 \times 10^{- 4} m^{2}$

$T h e f l u x ϕ = \vec{E} . \vec{Δ S} = E Δ S \cos θ = (\frac{σ}{2 \in_{0}}) (π r^{2}) \cos 60^{0}$

$= \frac{2 \times 10^{- 6} \times 3.14 \times 10^{- 4} \times (\frac{1}{2})}{2 \times 8.85 \times 10^{- 12}} = 17.74 N - m^{2} / C$

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