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Question
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10−22 C/m2. What is E:
- in the outer region of the first plate,
- in the outer region of the second plate, and
- between the plates?
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Solution
The situation is represented in the following figure.
A and B are two parallel plates close to each other. Outer region of plate A is labelled as I, the outer region of plate B is labelled as III, and the region between the plates, A and B, is labelled as II.
Charge density of plate A, σ = 17.0 × 10−22 C/m2
Charge density of plate B, σ = −17.0 × 10−22 C/m2
In regions, I and III, electric field E is zero. This is because the charge is not enclosed by the respective plates.
Electric field E in region II is given by the relation,
`"E" = sigma/in_0`
Where,
∈0 = Permittivity of free space = 8.854 × 10−12 N−1 C2 m−2
∴ `"E" = (17.0 xx 10^-22)/(8.854 xx 10^-12)`
= 1.92 × 10−10 N/C
Therefore, the electric field between the plates is 1.92 × 10−10 N/C.
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