Help with Electric Field on a Square Insulating Sheet?

[isabellef]

Homework Statement

A square insulating sheet whose sides have length L is held horizontally. The sheet has a charge of Q spread uniformly over its area.

a) Estimate the electric field at a point located a distance r_2 above the center of the sheet. Use the appropriate approximations based on the fact that r_2 >> L.

Homework Equations

E * dA = Q_encl/epsilon_0

The Attempt at a Solution

The area of the square sheet is L^2, which can go into the equation above. From that, I know that the electric field for r_2 << L is E = Q /(2*epsilon_0*L^2), but I can't seem to figure out the field for r_2 >> L.

Any suggestions?

 

[Spinnor]

From far away a sheet of paper looks like a spot or a point. The approximation I think they want is to treat the sheet of charge as a point charge? You got it from there?

 

[isabellef]

Not quite. Do you mind explaining a little further?

 

[Spinnor]

If you are far from a sheet of charge it does not matter what the orientation of the sheet of charge is the electric field still points towards you. Far from a distribution of charge the charge distribution can be approximated as a point charge.

 

[mateomy]

If you have any object that has a uniform charge density; as your sheet does, your object can be treated as a point particle if the radius is MUCH MUCH greater than the overall size of the initial object. That's what the r_2>>>L is telling you. You should know how to calculate the E-field for a point particle.

 

[isabellef]

Oh okay, now I understand. Thank you for the help!