Is My Integral Setup Correct for the Electric Field of a Square Sheet?

In summary, the electric field of a square sheet is a vector quantity that measures the strength and direction of the electric force per unit charge at any given point around the sheet. It can be calculated using the formula E = σ/2ε<sub>0</sub>, and its direction is always perpendicular to the sheet. The electric field decreases with distance according to the inverse square law and can be affected by the presence of other charges through the superposition principle.
  • #1
Shinobii
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Homework Statement


Field the electric field of a square sheet. I understand this is a simple problem, I just want to confirm I have the integral set up correctly.


Homework Equations


[tex] \vec{E} = \sigma z \int_{-a/2}^{a/2} \int_{-a/2}^{a/2} \frac{dx' \, dy'}{(x'^2 + y'^2 + z)^{3/2}} \hat{z}. [/tex]

I just want to double check if I have set up the integral correctly.
 
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  • #2
Looks good to me! [EDIT: In SI system there would be an overall factor of ##k = \frac{1}{4\pi\epsilon_0}##]
 
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FAQ: Is My Integral Setup Correct for the Electric Field of a Square Sheet?

What is the electric field of a square sheet?

The electric field of a square sheet is a measure of the strength and direction of the electric force per unit charge at any given point around the sheet. It is a vector quantity, meaning it has both magnitude and direction.

How is the electric field of a square sheet calculated?

The electric field of a square sheet can be calculated using the formula E = σ/2ε0, where σ is the surface charge density and ε0 is the permittivity of free space. This formula applies when the point of interest is at a distance greater than the length of one side of the sheet.

What is the direction of the electric field of a square sheet?

The direction of the electric field of a square sheet is always perpendicular to the sheet, pointing away from the sheet for positive charges and towards the sheet for negative charges.

How does distance affect the electric field of a square sheet?

The electric field of a square sheet decreases with distance from the sheet according to the inverse square law. This means that as the distance from the sheet doubles, the electric field strength decreases by a factor of four.

Can the electric field of a square sheet be affected by the presence of other charges?

Yes, the electric field of a square sheet can be affected by the presence of other charges. If there are other charged objects in the vicinity, the electric field will change based on the superposition principle, which states that the total electric field at any point is the sum of the electric fields due to each individual charge.

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