Surface Charge Density for Infinite Sheet of Charge

In summary, the surface charge density of the sheet on the y-axis is -10.35 micro Coulombs per meter2.
  • #1
eestep
36
0

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
 
Last edited:
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  • #2
Does it not cancel anyhow?
 
  • #3
eestep said:

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
How do I calculate surface charge density of sheet on y axis?
 
  • #5
eestep said:
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
I appreciate your assistance!
 

FAQ: Surface Charge Density for Infinite Sheet of Charge

1. What is surface charge density for an infinite sheet of charge?

Surface charge density for an infinite sheet of charge is the amount of charge per unit area on the surface of a sheet that extends infinitely in all directions. It is denoted by the symbol σ and has units of Coulombs per square meter (C/m2).

2. How is surface charge density calculated?

Surface charge density is calculated by dividing the total charge on the sheet by its surface area. The formula is σ = Q/A, where Q is the total charge and A is the surface area of the sheet. Alternatively, it can also be calculated by taking the limit as the area approaches zero of the charge enclosed by a closed surface divided by the area of the surface.

3. What is the significance of surface charge density for an infinite sheet of charge?

Surface charge density is a crucial concept in understanding the behavior of electric fields and potential around an infinite sheet of charge. It helps determine the strength of the electric field and the potential at any point in space. Furthermore, it is used in various applications such as in the design of capacitors and other electronic devices.

4. How does surface charge density affect the electric field around an infinite sheet of charge?

The surface charge density of an infinite sheet of charge determines the strength of the electric field around the sheet. The electric field is directly proportional to the surface charge density, meaning that an increase in surface charge density will result in a stronger electric field and vice versa. This is because a higher surface charge density means there is a higher concentration of charge per unit area, resulting in a stronger electric field.

5. Can surface charge density be negative?

Yes, surface charge density can be negative. This occurs when the charge on the sheet is negative, or when the direction of the electric field is opposite to the direction of the surface normal. In this case, the electric field and the surface charge density have opposite signs. However, it is important to note that the absolute value of the surface charge density is still the same regardless of its sign.

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