Electric field 0.1mm above charged plate.

[megr_ftw]

Homework Statement

A thin 0.08x0.08 meter copper plate is charged with 9*10^9 electrons. What are the strength and direction of the electric field 0.1mm above center of the top surface of the plate.

Homework Equations

n=Q/A
E=n/E_0

The Attempt at a Solution

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I found the linear charge density to be 2.25*10^-7 c/m^3 from the first equation above. I multiplied the number of electrons by the charge of a single electron and divided by the area.

Next I took the linear charge density and divided it by epsilon_0 to get a final charge of 25423.72 N/C.
I plugged this into webassign but it says that's wrong? could someone check this for me because I swear this is the right way to go about this problem
thanks

 

[Redbelly98]

E=n/E_0

That equation is for a pair of oppositely-charged plates.

For a single plate, it's

E = n/2ε_o​

They might want you to watch the number of significant figures in the answer you report, too.

Other than that, things look okay to me.

 

[tomcue]

I would like to verify the equations and steps used to solve this problem. The linear charge density equation (n=Q/A) is correct, but the value for the linear charge density seems to be incorrect. The correct value should be 1.125*10^-7 C/m^2, calculated by dividing the total charge (9*10^9 electrons) by the area (0.08x0.08 m^2).

The next equation used (E=n/E_0) seems to be incorrect. The correct equation for electric field is E=kQ/r^2, where k is the Coulomb's constant, Q is the charge, and r is the distance from the charged object.

Using this equation, the electric field at a distance of 0.1 mm (0.0001 m) above the center of the top surface of the plate would be calculated as follows:

E = (9*10^9 * 1.125*10^-7) / (0.0001)^2 = 9*10^16 N/C

The direction of the electric field would be pointing away from the charged plate, in a direction perpendicular to the surface.

I would also like to point out that the units for electric field are N/C, not C/N as mentioned in the attempt at a solution.

I hope this helps in solving the problem correctly. If you continue to have trouble, please provide more information or show your work so that I can assist you further.