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 $17.0\times 10^{-22}\; C/m^2$. What is $E$:
$(a)$ in the outer region of the first plate,
$(b)$ in the outer region of the second plate, and
$(c)$ between the plates?
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 $17.0\times 10^{-22}\; C/m^2$. What is $E$:
$(a)$ 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 $A , \sigma=17.0 \times 10^{-22} \,C / m ^{2}$
Charge density of plate $B , \sigma=-17.0 \times 10^{-22} \,C / m ^{2}$
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,
$E=\frac{\sigma}{\varepsilon_{0}}$
Where, $\varepsilon_{0}=$ Permittivity of free space $=8.854 \times 10^{-12}\, N ^{-1} \,C ^{2} \,m ^{-2}$
$=1.92 \times 10^{-10} \,N / C$
$E=\frac{17.0 \times 10^{-22}}{8.854 \times 10^{-12}}$
Therefore, electric field between the plates is $1.92 \times 10^{-10}\; N / C$
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