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

In summary, three charged boards are positioned on the x-axis, with the middle board at x=0 and a positive charge density of σ. The other two boards are located at x=d and x=-2d and are grounded. The area of the boards is A, which is significantly larger than d. The electric field is divided in a 2:1 ratio from x=0 to x=d and x=-2d, respectively. To find the total force on the middle board, the formula F=σ*(E1-E2) is used, resulting in (4/3)∏*k*(σ^2)*A. However, the correct answer is (2/3)∏*k*(σ
  • #1
axcelenator
33
0
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!
 
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  • #2
See your other thread with the same problem. ehild
 

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

What is the total force on a charge plate?

The total force on a charge plate refers to the net force exerted on the plate due to the presence of multiple charges. This force can be calculated by summing up the individual forces that each charge exerts on the plate.

How is the total force on a charge plate calculated?

The total force on a charge plate is calculated using Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. By applying this law to all the charges on the plate, the total force can be determined.

Does the total force on a charge plate depend on the magnitude of the charges?

Yes, the magnitude of the charges on the plate directly affects the total force. According to Coulomb's law, the force between two charges increases as their magnitudes increase. Therefore, the greater the magnitude of the charges on the plate, the greater the total force will be.

Can the total force on a charge plate be negative?

Yes, the total force on a charge plate can be negative. This would occur if the individual forces exerted by the charges on the plate are in opposite directions. In this case, the total force would be the vector sum of these forces, resulting in a negative value.

What factors can affect the total force on a charge plate?

The total force on a charge plate can be affected by the number and magnitude of charges on the plate, as well as the distance between the charges. Additionally, the presence of other charges or external electric fields in the surrounding environment can also impact the total force on the plate.

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