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Surface Charge Density for Infinite Sheet of Charge

  • Thread starter eestep
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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


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


The Attempt at a Solution


Fex=-qE=-q[tex]\sigma[/tex]x/2[tex]\epsilon[/tex]0
Fey=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]xtan[tex]\theta[/tex]=7.8tan143
 
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Answers and Replies

  • #2
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Does it not cancel anyhow?
 
  • #3
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


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


The Attempt at a Solution


Fex=-qE=-q[tex]\sigma[/tex]x/2[tex]\epsilon[/tex]0 This should be Fey .
Fey=qE=q[tex]\sigma[/tex]y/2[tex]\epsilon[/tex]0 This should be Fex .
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]xtan[tex]\theta[/tex]=7.8tan143
The sheet with known charge, lying in the x-z plane, produces an electric field parallel to the y-axis.
 
  • #4
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How do I calculate surface charge density of sheet on y axis?
 
  • #5
SammyS
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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.
 
  • #6
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I appreciate your assistance!
 

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