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I have a question based on a task given by my physics textbook:

Two identical elongated objects with identical charge are put in front of each other as in the attached picture. The objects are 0.03 metre long and 0.02 metre wide each. The electric field between them is 8000 N/C. The question then is: how much charge should be given to these objects for that particular electric field to come about.

The answer is based on the formulas E=σ/εo (sorry, the o should be in subscript); and σ=q/A. I understand the logic fully and actually got the answer right, except for one detail: in the book they use the A of only one of the two charged objects (0.03 x 0.02 m = 0.006 m) for the formula; whereas I doubled it to 0.012 m, seeing that there are two objects. Given that the formula E=σ/εo was explained earlier in the book as an amalgamation of E=σ/2εo + σ/2εo = σ/εo, where each σ/2εo refers to one of two identical objects placed opposite each other with opposite charge (as in the exercise), this seemed like the logical thing to do.

Can anybody explain what I am getting wrong?

enter image description here

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Each charged plate on its own creates a field with intensity $E=\frac{\sigma}{2 \varepsilon_0}=\frac{q}{2A\varepsilon_0}$. Combining both, with $q$ being the charge of each plate and $A$ the area of each plate, you get...

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If a plate has charge density $\sigma$ on one side, the field it'll produce, on that side, will be $\frac \sigma {\epsilon_0}$ and will go to infinity.

Adding another, parallel, plate with the opposite charge of the same density on the side facing the first plate, does not change that field: the charges on the second plate will just terminate the field lines coming from the charges on the first plate, and vise versa, keeping the field from going to infinity.

A tricky part here is the charge on a standalone plate does not stay on one side, but rather gets distributed between the two sides, with the resulting field on each side $\frac \sigma {2\epsilon_0}$.

When two such plates are brought very close to each other, practically all charges, due to the mutual attraction, migrate on the inner sides, resulting in the doubling of the field.

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