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 $17.0 \times 10^{-22} \,Cm ^{-2}$.
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.
$E _{ I }= E _{A}+ E _{B}=\frac{\sigma}{2 \varepsilon_{0}}+\left(-\frac{\sigma}{2 \varepsilon_{0}}\right)=0$