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## Homework Statement

An infinite sheet of charge with a surface charge density of +7.8 micro-Coulomb/m

^{2}lies on x-axis (technically in x-z plane). Another infinite sheet of charge with an unknown charge density lies on y-axis (technically in y-z plane). A positive point charge is placed in first quadrant and total electric force on this charge due to infinite sheets is directed at an 143 degree angle when measured counter-clockwise from positive x axis. What is surface charge density of sheet on y-axis in micro-Coulomb/m

^{2}? Answer is -10.35.

## Homework Equations

[tex]\sigma[/tex]=dq/dA

## The Attempt at a Solution

F

_{ex}=-qE=-q[tex]\sigma[/tex]

_{x}/2[tex]\epsilon[/tex]

_{0}

F

_{ey}=qE=q[tex]\sigma[/tex]

_{y}/2[tex]\epsilon[/tex]

_{0}

tan[tex]\theta[/tex]=(q[tex]\sigma[/tex]

_{y}/2[tex]\epsilon[/tex]

_{0})/(q[tex]\sigma[/tex]

_{x}/2[tex]\epsilon[/tex]

_{0})

tan[tex]\theta[/tex]=[tex]\sigma[/tex]

_{y}/[tex]\sigma[/tex]

_{x}

[tex]\sigma[/tex]

_{y}=[tex]\sigma[/tex]

_{x}tan[tex]\theta[/tex]=7.8tan143

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