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Electricity and Magnetism

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Electric Field Due to Two Perpendicular Planes of Charge

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Two infinite sheets of uniform surface charge density are oriented perpendicularly to each other as shown in the figure below. One sheet with uniform surface charge density $\sigma_1 = 12.0 \:\mu \rm C m^{-2}$ lies in the $y-z$ plane. The second sheet with uniform surface charge density $\sigma_2 = 20.0 \:\mu \rm C m^{-2}$ lies in the $x-z$ plane.

Created for Albert.io. Copyright 2016. All rights reserved.

What is the total electric field at the point P with coordinates $x=1.5 \: \rm m$, $y = 2.5 \:\rm m$, and $z=0 \: \rm m$?

A

$(12.0 \hat x + 20.0 \hat y) \times 10^{-6}$ N/C

B

$(6.00\hat x + 10.0 \hat y) \times 10^{-6}$ N/C

C

$(6.78\hat x + 11.3 \hat y) \times 10^{5}$ N/C

D

$(13.56\hat x + 22.6 \hat y) \times 10^{5}$ N/C

E

$(3.39\hat x + 5.65 \hat y) \times 10^{5}$ N/C