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**Electrostatics -- 3rd plate inserted into parallel plate capacitor**

## Homework Statement

This question is from the book by I.S Grant and W.R Phillips on Electromagnetism. Two large parallel plates of area A and distance d apart are maintained at potentials 0 and V. A third similar plate, carrying a charge q, is isolated from the other two and placed midway between them. What is the potential of this plate?

## Homework Equations

V = -∫

**E**.

**dl**

**E**=σ/d

σ=q/A

## The Attempt at a Solution

The plate is placed half way between the two plates so I integrated the electric field between 0 and 1/2d. This gave me the potential as σd/2ε[itex]_{0}[/itex]. I know that σ is simply the charge on the plate q divided by the area A. Substituting this into my answer gives qd/2ε[itex]_{0}[/itex]A. The final answer however, is 1/2V plus the answer which I obtained. I am not sure if what I have done is correct or where the 1/2V came from. Any help would be appreciated.