In $X - Y$ plane, there is surface charge density of $5 \times 10^{- 16} C / m^{2}$ on a long uniformly charged sheet. A circular loop of radius $0.1 m$ makes an angle of $60^{o}$ with Z-axis. Determine the electric flux through the loop.

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Solution

Given $σ = 5.0 \times 10^{- 16} C / m^{- 2}, r = 0.1 m$
$θ = 60^{0}$ electric field due to layer of plane charge
$E = \frac{σ}{2 ϵ_{0}}$
Flux passing through circular surface
$ϕ_{E} = E Δ S c o s θ$
$= \frac{σ}{2 ϵ_{0}} \times π r^{2} c o s θ$
$= \frac{5.0 \times 10^{- 16} \times 3.14 \times (0.1)^{2} c o s 60^{0}}{2 \times 8.85 \times 10^{- 12}}$
$= 4.44 \times 10^{- 7} N m^{2} C^{- 1}$

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