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 $17.0\times 10^{-22}C{m}^{-2}$.
What is $E$ in the outer region of the first plate?

• A. $17\times 10^{-22}N/C$
• B. $1.5\times 10^{-15}N/C$
• C. $1.9\times 10^{-10}N/C$
• D. Zero

Answer 1

Answer: (D)

There are two plates $A$ and $B$ having surface charge
densities ${\sigma }_A=17.0\times 10^{-22}C/m^2$ on $A$ and
${\sigma }_B=-17.0\times 10^{-22}C/m^2$ on $B$, respectively.

According to Gauss' theorem, if the plates have same surface charge density but having opposite signs, then the electric field in region $I$ is zero.
$E_I=E_A+E_B=\frac{\sigma }{2{\epsilon }_0}+\left(-\frac{\sigma }{2{\epsilon }_0}\right)=0$