How Do You Calculate the Total Force on a Charged Plate in a Three-Board System?

[axcelenator]

Three boards are in the x axis. the middle one is in x=0 and charged in a positive sign density is: σ. the other 2 boards are in : x=d and x=-2d. This 2 boards are grounded. The area of the boards is A (A>>d).

I found that on the middle plate the charge is divided in 2:1 ratio: The electric field from X=0 to X=d is:E1 = (8/3)*∏*k*σ
and from X=0 to X=-2d is: E2 = (-4/3)*∏*k*σ.
If I want to find the total force on the middle plat should I do: F=σ*(E1-E2) ?? I get (4/3)∏*k*(σ^2)*A

but the answer says: F=(2/3)∏*k*(σ^2)*A

thanks!

 

[ehild]

See your other thread with the same problem. ehild