An infinite plane in the xz plane carries a uniform surface charge density σ1 = 8.85 nC/m2. A second infinite plane carrying a uniform charge density σ2 = 17.7 nC/m2 intersects the xz plane at the z axis and makes an angle of 60° with the xz plane as shown in Figure. The electric field in the xy plane.

Engineering

Physics

Electric Field and Gauss Law

Question

An infinite plane in the xz plane carries a uniform surface charge density σ₁ = 8.85 nC/m². A second infinite plane carrying a uniform charge density σ₂ = 17.7 nC/m² intersects the xz plane at the z axis and makes an angle of 60° with the xz plane as shown in Figure. The electric field in the xy plane.

at x = 2m, y = 6 m is $500 \sqrt{7}$ N/C

at x = 6m, y = 2m is $500 \sqrt{3}$ N/C

at x = –5m, y = 0 is $500 \sqrt{3}$ N/C

at x = –1m, y = –1m is $500 \sqrt{7}$ N/C

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$E_{1} = \frac{σ_{1}}{2 ϵ_{0}} = \frac{8.85 \times 10^{- 9}}{2 \times 8.85 \times 10^{- 12}} = 500 NC$

$E_{2} = \frac{σ_{2}}{2 ϵ_{0}} = 1000 N / C$

$E = \sqrt{500^{2} + 1000^{2} \times 500 \times 1000 \times \frac{1}{2}} = 500 \sqrt{1 + 4 - 2} = 500 \sqrt{3} N / C$

$E = \sqrt{500^{2} + 1000^{2} + 2 \times 500 \times 1000 \times \frac{1}{2}} = 500 \sqrt{1 + 4 + 2} = 500 \sqrt{7} N ? C$

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