Electric field at (0,0) for this charged square conductor

In summary: This solution is true ? According to this,the electric field is 0 on anyplace in the square conductor.Yes this solution is correct.
  • #1
requied
98
3
Homework Statement
If this figure below is a conductor, what will be the electric field at (0,0) for the square charge distribution
Relevant Equations
Gauss' Law
1590920527485.png


Can we assume that square charge resembles a sphere shell, and think like electric field at sphere shell's center is 0.
 
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  • #2
1590922130848.png

This solution is true ? According to this,the electric field is 0 on anyplace in the square conductor.
 
  • #3
No this solution is not correct. You can't take the E out of the integral, as you do in the 2nd line, because the spherical gaussian surface is not symmetrical with respect to the square charge density.
 
  • #4
You are only asked for the field at (0,0). Isn't the answer obvious by symmetry?
 
  • #5
haruspex said:
You are only asked for the field at (0,0). Isn't the answer obvious by symmetry?
Yeah it is obvious but I must attach an explain and show the calculations. Have you any offer to do it by this way? Or maybe a figure which can explain.
 
  • #6
Delta2 said:
You can't take the E out of the integral, as you do in the 2nd line, because the spherical gaussian surface is not symmetrical with respect to the square charge density.
I have a trouble with square shape symmetry. How can I come through of it? Or maybe I don't have to show calculations, just draw a figure which can explain the logic.
 
  • #7
requied said:
I have a trouble with square shape symmetry. How can I come through of it? Or maybe I don't have to show calculations, just draw a figure which can explain the logic.
Well the truth is that this square shaped charge density doesn't offer us with any symmetry that would be useful in Gauss's law. You just can't use Gauss's law (with any possible gaussian surface) to solve for the electric field in the interior.

However the point (0,0) has a special symmetry. To see this symmetry , try to draw the electric field vectors at the center due to each of the 4 sides of the square. You ll draw 4 vectors and then you ll have to argue how they cancel out in pairs. And then you ll conclude that the E-field at the center is indeed zero.
 
  • #8
Delta2 said:
try to draw the electric field vectors at the center due to each of the 4 sides of the square. You ll draw 4 vectors and then you ll have to argue how they cancel out in pairs.
I've been thinking the same thing from the beginning. I'll solve this by this way, I hope it works for getting some point :) Thank you for attention.
 
  • #9
requied said:
Yeah it is obvious but I must attach an explain and show the calculations. Have you any offer to do it by this way? Or maybe a figure which can explain.
You can use the symmetry in your equations. There is no need to solve any integral. Just write the integrals down and collect up terms that cancel.
 

Related to Electric field at (0,0) for this charged square conductor

1. What is an electric field?

An electric field is a physical quantity used to describe the force exerted on a charged particle by other charged particles in its vicinity. It is represented by electric field lines and is measured in units of volts per meter (V/m).

2. How is the electric field at (0,0) for a charged square conductor calculated?

The electric field at a point is calculated by dividing the force exerted on a test charge at that point by the magnitude of the test charge. For a charged square conductor, the electric field at (0,0) can be calculated by summing up the contributions from each side of the conductor using Coulomb's law.

3. What factors affect the electric field at (0,0) for a charged square conductor?

The electric field at (0,0) for a charged square conductor is affected by the magnitude and distribution of charges on the conductor, the distance from the conductor, and the presence of other nearby charged objects.

4. Is the electric field at (0,0) for a charged square conductor constant?

No, the electric field at (0,0) for a charged square conductor is not constant. It varies depending on the location and orientation of the test charge, as well as the factors mentioned in the previous answer.

5. How is the direction of the electric field at (0,0) for a charged square conductor determined?

The direction of the electric field at (0,0) for a charged square conductor is determined by the direction of the force that would be exerted on a positive test charge placed at that point. The direction of the electric field lines always points away from positive charges and towards negative charges.

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