# Surface Charge Density for Infinite Sheet of Charge

## Homework Statement

An infinite sheet of charge with a surface charge density of +7.8 micro-Coulomb/m2 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/m2? Answer is -10.35.

## Homework Equations

$$\sigma$$=dq/dA

## The Attempt at a Solution

Fex=-qE=-q$$\sigma$$x/2$$\epsilon$$0
Fey=qE=q$$\sigma$$y/2$$\epsilon$$0
tan$$\theta$$=(q$$\sigma$$y/2$$\epsilon$$0)/(q$$\sigma$$x/2$$\epsilon$$0)
tan$$\theta$$=$$\sigma$$y/$$\sigma$$x
$$\sigma$$y=$$\sigma$$xtan$$\theta$$=7.8tan143

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Does it not cancel anyhow?

SammyS
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## Homework Statement

An infinite sheet of charge with a surface charge density of +7.8 micro-Coulomb/m2 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/m2? Answer is -10.35.

## Homework Equations

$$\sigma$$=dq/dA

## The Attempt at a Solution

Fex=-qE=-q$$\sigma$$x/2$$\epsilon$$0 This should be Fey .
Fey=qE=q$$\sigma$$y/2$$\epsilon$$0 This should be Fex .
tan$$\theta$$=(q$$\sigma$$y/2$$\epsilon$$0)/(q$$\sigma$$x/2$$\epsilon$$0)
tan$$\theta$$=$$\sigma$$y/$$\sigma$$x
$$\sigma$$y=$$\sigma$$xtan$$\theta$$=7.8tan143
The sheet with known charge, lying in the x-z plane, produces an electric field parallel to the y-axis.

How do I calculate surface charge density of sheet on y axis?

SammyS
Staff Emeritus
Homework Helper
Gold Member
How do I calculate surface charge density of sheet on y axis?
The vector you said was in the x direction is in the y direction.

The vector you said was in the y direction is in the x direction.

Correcting this will give you the right answer.