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 $17.0 \times 10^{-22} \mathrm{C} / \mathrm{m}^{2}$. What is $\mathrm{E}$ :
(a) in the outer region of the first plate,
(b) in the outer region of the second plate, and
(c) between the plates?
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, 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 $\mathrm{A}, \sigma=17.0 \times 10^{-22} \mathrm{C} / \mathrm{m}^{2}$
Charge density of plate $B, \sigma=-17.0 \times 10^{-22} \mathrm{C} / \mathrm{m}^{2}$
In the regions, I and III, electric field E is zero. This is because charge is not enclosed by the respective plates.
Electric field E in region II is given by the relation,
$E=\frac{\sigma}{\epsilon_{0}}$
Where,
$\epsilon_{0}=$ Permittivity of free space $=8.854 \times 10^{-12} \mathrm{~N}^{-1} \mathrm{C}^{2} \mathrm{~m}^{-2}$
$\therefore E=\frac{17.0 \times 10^{-22}}{8.854 \times 10^{-12}}$
$=1.92 \times 10^{-10} \mathrm{~N} / \mathrm{C}$
Therefore, electric field between the plates is $1.92 \times 10^{-10} \mathrm{~N} / \mathrm{C}$.